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Numerical analysis of harbor oscillation under effect of fluctuating tidal level and varying harbor layout
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Numerical analysis of harbor oscillation under effect of fluctuating tidal level and varying harbor layout
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Content
NUMERICAL ANALYSIS OF HARBOR OSCILLATION
UNDER EFFECT OF FLUCTUATING TIDAL LEVEL
AND VARYING HARBOR LAYOUT
by
Shentong Lu
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
CIVIL ENGINEERING
December 2014
Copyright 2014 Shentong Lu
ii
I would like to dedicate this dissertation work to my beloved family.
iii
ACKNOWLEDGEMENTS
First of all, I would like to express my sincere gratitude to my advisor, Dr. Jiin-Jen Lee,
for his academic, moral, and financial support throughout my study time in University of
Southern California. I really appreciate his way of guidance, which goes beyond academy
to be the education of life.
I would like to thank Dr. Patrick Lynett, Dr. Costas Synolakis, and Prof. Martin Eskijian
in University of Southern California for their academic support. Much gratitude to David
Dykstra in Moffatt & Nichol Engineers, Mikkel Andersen and Dale Kerper in DHI,
Nikos Kalligeris, and Aykut Ayca in USC Tsunami Research Center for their technical
support. Without their precious suggestion and help, this work would encounter much
more difficulties.
Thanks my fellows, Ziyi Huang, Yuan-Hung Tan, Mehrdad Bozorgnia, Amir Eftekharian,
Maryam Ghadiri, Hyoung-Jin Kim, Chanin Chaun-Im, Zhiqing Kou, Hadi Meidani, Iman
Yadegaran, Ahmed Mantawy, and Weixuan Li for all your supports.
Salute to John Cornett, Paul Schwartz, Nate Frey, Troy Poole, Daniel O’connell, David
Ritz, Mathew Yancy, and Henry Chang in the Foundation for Cross-Connection Control
and Hydraulic Research.
iv
TABLE OF CONTENTS
DEDICATION ………………………………………………………………………...… ii
ACKNOWLEDGEMENTS …………………………………………………………….. iii
LIST OF TABLES …………………………………….……………...….…....….…… viii
LIST OF FIGURES ………………………………………………………………..…… ix
ABSTRACT ……………………………………………………………………...…..… xx
CHAPTER 1: INTRODUCTION ………………………………………………….…… 1
1.1 Background ………………………………………………………………..…… 1
1.2 Objective and Scope of Present Study ……………………………………….… 4
CHAPTER 2: LITERATURE SURVEY ………………………………………….….… 7
2.1 Theoretical Construction ……………………………………………….....……. 7
2.2 Previous Research …………………………………………………………….. 11
2.3 Observation and Analysis ………………………………………………..….... 13
CHAPTER 3: METHODOLOGY AND MODEL …………………………………….. 18
3.1 Governing Equation …………………………………………………………... 19
3.2 Boundary Conditions and Initial Conditions …………………………………. 21
3.3 Pretreatment and Discretization …………………………………………….… 24
3.3.1 ADI scheme ……………………………………………………………. 25
3.3.2 Solving method ………………………………………………………… 27
3.4 Mapping Projection and Bathymetry …………………………………………. 28
3.5 Incident Wave ………………………………………………………………… 32
v
CHAPTER 4: MODEL VERIFICATION ……………………………………...……… 34
4.1 Experimental Setup …………………………………………………………… 35
4.2 Numerical Model Setup …………………………………………………….… 37
4.2.1 Computation Power ……………………………………………………. 37
4.2.2 Choice of Resolution and Time Step …………………………………... 38
4.2.3 Choice of Boundary Conditions ……………………………………...… 39
4.2.4 Internal Wave Generation Line …………………………………...……. 41
4.3 Group A: Rectangular Harbor ………………………………………………… 42
4.3.1 Case #1 …………………………………………………………………. 43
4.3.2 Case #2 …………………………………………………………………. 53
4.3.3 Case #3 ………………………………………………………...……….. 63
4.3.4 Case #4 ……………………………………………………………….… 71
4.4 Group B: Trapezoidal Harbor ………………………………………...………. 79
4.4.1 Case #5 …………………………………………………………….…… 80
4.4.2 Case #6 …………………………………………………………….…… 88
4.5 Summary ……………………………………………………………………… 98
CHAPTER 5: HARBOR OSCILLATION ON MEAN TIDAL LEVEL ……………... 99
5.1 Crescent City Harbor, California ……………………………………...…..… 100
5.1.1 Model Setup …………………………………………………….…..… 101
5.1.2 Results ………………………………………………………...………. 103
5.2 Los Angeles/Long Beach Port, California ……………………………...…… 106
5.2.1 Model Setup ………………………………………………...………… 107
5.2.2 Results …………………………………………………………...……. 109
5.3 San Diego Harbor, California ……………………………………………….. 112
5.3.1 Model Setup ………………………………………………...………… 113
5.3.2 Results ………………………………………………………...………. 115
5.4 Pago Pago Harbor, American Samoa ……………………………….……….. 118
vi
5.4.1 Model Setup ……………………………………………………...…… 119
5.4.2 Results ……………………………………………………………...…. 121
5.5 Summary ……………………………………………………………..……… 124
CHAPTER 6: FLUCTUATING TIDAL LEVEL AND VARYING LAYOUT …..… 125
6.1 Observed Phenomenon in Reality ……………………………………..……. 126
6.2 Possible Factors …………………………………………………………..…. 132
6.3 White Noise Analysis on Different Tidal Levels ………………………..….. 133
6.3.1 Crescent City Harbor ……………………………………………...….. 133
6.3.2 Los Angeles/Long Beach Port ………………………………..………. 147
6.3.3 San Diego Harbor …………………………………………………..… 159
6.4 White Noise Analysis on Fluctuating Tidal Level ………………………..… 171
6.4.1 Crescent City Harbor …………………………………………….…… 171
6.4.2 Los Angeles/Long Beach Port ………………………………..………. 181
6.4.3 San Diego Harbor ……………………………………………..……… 187
6.5 Summary …………………………………………………………..………… 193
CHAPTER 7: INVESTIGATION OF HISTORICAL OSCILLATION CASES ……. 194
7.1 Source of Data ………………………………………………………………. 194
7.2 Tsunami Caused by Chile Earthquake on Feb. 27
th
, 2010 ………………….. 195
7.2.1 Crescent City Harbor ……………………………………………...….. 195
7.2.2 Los Angeles/Long Beach Port ………………………………….…….. 198
7.2.3 San Diego Harbor ………………………………………………….…. 201
7.3 Tsunami Caused by Japan Earthquake on Mar. 11
th
, 2011 ……………….… 204
7.3.1 Crescent City Harbor ……………………………………………...….. 204
7.3.2 Los Angeles/Long Beach Port ………………………………….…….. 209
7.3.3 San Diego Harbor ……………………………………………….……. 212
7.4 Summary …………………………………………………………………….. 215
vii
CHAPTER 8: CONCLUSION …………………………………………..…………… 216
REFERENCES ………………………………………………………………..……… 219
viii
LIST OF TABLES
Table 4.1 The configuration of computation power in the present study …………...… 37
Table 4.2 The resolution and time step for water basin and real harbor ………………. 38
Table 4.3 The variable factors of harbor models in Group A ……………………...….. 42
Table 4.4 Dimensions of the harbor models in Case #1 ………………………………. 43
Table 4.5 Dimensions of the harbor models in Case #2 ……………………...……….. 53
Table 4.6 Dimensions of the harbor models in Case #3 ……………………...……….. 63
Table 4.7 Dimensions of the harbor models in Case #4 ………………………...…….. 71
Table 4.8 The characters of harbor models in Group B ……………………………..… 79
Table 4.9 Dimensions of the harbor models in Case #5 ………………………………. 80
Table 4.10 Dimensions of the harbor models in Case #6 ……………………………... 88
Table 6.1 Factors that affects the fundamental frequency of a harbor …………….…. 132
Table 6.2 Chosen tidal levels of Crescent City harbor ……………………….…….… 133
Table 6.3 Chosen tidal levels of Los Angeles/Long Beach Port ………………...…… 147
Table 6.4 Chosen tidal levels of San Diego harbor …………………….…………..… 159
Table 7.1 Three Types of Data of Concern …………………………………..….…… 194
ix
LIST OF FIGURES
Figure 1.1 Vessel damage caused by Tohoku tsunami on March 11
th
, 2011 ……...….. 2
Figure 2.1 The tsunami generated by Ligurian earthquake on Feb. 23
rd
, 1887 …....… 14
Figure 2.2 Source functions of (a) the October 2000 storm;
(b) the Peru 2000 tsunami oscillations on the B.C coast. ………………... 15
Figure 2.3 The observed inundation height and run-up height along east
Japanese coast. View (a) is overall Japan, and View (b) is
above Seidai ………………………………………………………..…..….. 17
Figure 3.1 The sketch of an arbitrary shape harbor geometry ………………….…….. 21
Figure 3.2 A typical CV and the notation used for Cartesian 2D grid ……………..…. 25
Figure 3.3 The chart of Crescent City harbor (CA) before projection ………………... 29
Figure 3.4 A typical process of normal Mercator projection ………………………..... 30
Figure 3.5 The map of Crescent City harbor (CA) after projection ………………...… 31
Figure 4.1 Overall view of the water basin ………………………………………...…. 35
Figure 4.2 The wave generator ……………………………………………………..… 35
Figure 4.3 A rectangular harbor model ………………………………………………. 36
Figure 4.4 (a) The integrated system to control, receive, and monitor signal
(b) Probe to measure surface elevation …………………………………… 36
Figure 4.5 The distribution of sponge layer coefficient ………………………………. 39
Figure 4.6 The fully reflective boundary ……………………………………………… 40
Figure 4.7 Internal wave generation line …………………………………………..….. 41
Figure 4.8 A typical plan view of the harbor in case 1 ………………………...……… 43
Figure 4.9 Incident wave profile in Case #1 …………………………………………... 44
Figure 4.10 The spatially discretized bathymetry of model 1 in Case #1 ………….….. 45
Figure 4.11 The present numerical solution at probe gauge for Case 1_1 ……...….…. 46
Figure 4.12 Comparison between the present numerical solution and experiment …… 46
Figure 4.13 The spatially discretized bathymetry of model 2 in Case #1 ……….…….. 47
x
Figure 4.14 The present numerical solution at probe gauge for Case 1_2 ……...…..… 48
Figure 4.15 Comparison between the present numerical solution and experiment …… 48
Figure 4.16 The spatially discretized bathymetry of model 3 in Case #1 …………….. 49
Figure 4.17 The present numerical solution at probe gauge for Case 1_3 ………….… 50
Figure 4.18 Comparison between the present numerical solution and experiment ........ 50
Figure 4.19 The spatially discretized bathymetry of model 4 in Case #1 ………….…. 51
Figure 4.20 The present numerical solution at probe gauge for Case 1_4 …………… 52
Figure 4.21 Comparison between the present numerical solution and experiment …... 52
Figure 4.22 A typical plan view of the harbor in case 2 …………………………..….. 53
Figure 4.23 Incident wave profile in Case #2 …………………………………….…… 54
Figure 4.24 The spatially discretized bathymetry of model 1 in Case #2 …………….. 55
Figure 4.25 The present numerical solution at probe gauge for Case 2_1 ……...….…. 56
Figure 4.26 Comparison between the present numerical solution and experiment …… 56
Figure 4.27 The spatially discretized bathymetry of model 2 in Case #2 ………….…. 57
Figure 4.28 The present numerical solution at probe gauge for Case 2_2 …...……..… 58
Figure 4.29 Comparison between the present numerical solution and experiment ….... 58
Figure 4.30 The spatially discretized bathymetry of model 3 in Case #2 …………..…. 59
Figure 4.31 The present numerical solution at probe gauge for Case 2_3 ………...….. 60
Figure 4.32 Comparison between the present numerical solution and experiment ….... 60
Figure 4.33 The spatially discretized bathymetry of model 4 in Case #2 ……………... 61
Figure 4.34 The present numerical solution at probe gauge for Case 2_4 ………...….. 62
Figure 4.35 Comparison between the present numerical solution and experiment ….... 62
Figure 4.36 A typical plan view of the harbor in case 3 ………………………………. 63
Figure 4.37 The spatially discretized bathymetry of the only
harbor model in Case #3 ………………………………………….……… 64
Figure 4.38 Incident wave profile of scenario 1 in Case #3 ……………………….….. 65
Figure 4.39 The present numerical solution at probe gauge for Case 3_1 ……………. 66
xi
Figure 4.40 Comparison between the present numerical solution and experiment ….... 66
Figure 4.41 Incident wave profile of scenario 2 in Case #3 …………………………... 67
Figure 4.42 The present numerical solution at probe gauge for Case 3_2 ……………. 68
Figure 4.43 Comparison between the present numerical solution and experiment …… 68
Figure 4.44 Incident wave profile of scenario 3 in Case #3 ……………………….….. 69
Figure 4.45 The present numerical solution at probe gauge for Case 3_3 …………..... 70
Figure 4.46 Comparison between the present numerical solution and experiment …… 70
Figure 4.47 (a). A typical plan view of the harbor in case 4
(b). A typical side view of the harbor in case 4 …………………………... 71
Figure 4.48 The spatially discretized bathymetry of the only
harbor model in Case #4 ……………………………………………….… 72
Figure 4.49 Incident wave profile of scenario 1 in Case #4 ……………………….….. 73
Figure 4.50 The present numerical solution at probe gauge for Case 4_1 …...…….…. 74
Figure 4.51 Comparison between the present numerical solution and experiment …… 74
Figure 4.52 Incident wave profile of scenario 2 in Case #4 ………………………...… 75
Figure 4.53 The present numerical solution at probe gauge for Case 4_2 ……….....… 76
Figure 4.54 Comparison between the present numerical solution and experiment …… 76
Figure 4.55 Incident wave profile of scenario 3 in Case #4 ……………………….….. 77
Figure 4.56 The present numerical solution at probe gauge for Case 4_3 ………….… 78
Figure 4.57 Comparison between the present numerical solution and experiment ….... 78
Figure 4.58 A typical plan view of the harbor in case 5 ……………………………… 80
Figure 4.59 The spatially discretized bathymetry of the only
harbor model in Case #5 ………………………………………………..... 81
Figure 4.60 Incident wave profile of scenario 1 in Case #5 ……………………..……. 82
Figure 4.61 The present numerical solution at probe gauge for Case 5_1 ……….....… 83
Figure 4.62 Comparison between the present numerical solution and experiment ….... 83
Figure 4.63 Incident wave profile of scenario 2 in Case #5 ………………………...… 84
Figure 4.64 The present numerical solution at probe gauge for Case 5_2 ……...…….. 85
xii
Figure 4.65 Comparison between the present numerical solution and experiment ….... 85
Figure 4.66 Incident wave profile of scenario 3 in Case #5 …………………………... 86
Figure 4.67 The present numerical solution at probe gauge for Case 5_3 ……….....… 87
Figure 4.68 Comparison between the present numerical solution and experiment ….... 87
Figure 4.69 A typical plan view of the harbor in case 6 ………………………………. 88
Figure 4.70 Incident wave profile in Case #6 …………………………………………. 89
Figure 4.71 The spatially discretized bathymetry of model 1 in Case #6 ……….…….. 90
Figure 4.72 The present numerical solution at probe gauge for Case 6_1 ……...…….. 91
Figure 4.73 Comparison between the present numerical solution and experiment …… 91
Figure 4.74 The spatially discretized bathymetry of model 2 in Case #6 ……………... 92
Figure 4.75 The present numerical solution at probe gauge for Case 6_2 …...……..… 93
Figure 4.76 Comparison between the present numerical solution and experiment ….... 93
Figure 4.77 The spatially discretized bathymetry of model 3 in Case #6 ………….….. 94
Figure 4.78 The present numerical solution at probe gauge for Case 6_3 ……...…..… 95
Figure 4.79 Comparison between the present numerical solution and experiment …… 95
Figure 4.80 The spatially discretized bathymetry of model 4 in Case #6 …………...… 96
Figure 4.81 The present numerical solution at probe gauge for Case 6_4 ……………. 97
Figure 4.82 Comparison between the present numerical solution and experiment …… 97
Figure 5.1 (a) Crescent City on the West Coast; (b) & (c) Zoom-in …………..…….. 100
Figure 5.2 The layout and bathymetry of Crescent City on mean tidal level (MTL) ... 101
Figure 5.3 The incident wave for white noise analysis in Crescent City harbor …….. 102
Figure 5.4 The predicted response at tidal station in
Crescent City harbor (south source) ……………………………………... 103
Figure 5.5 The predicted response at tidal station in
Crescent City harbor (west source) …………………………………….… 103
Figure 5.6 Spectra of oscillation in Crescent City harbor ………………………….… 104
Figure 5.7 Amplification factor at tidal gauge with respect to kl ……………………. 105
xiii
Figure 5.8 (a) LA/LB port on the West Coast; (b) & (c) Zoom-in ……………..……. 106
Figure 5.9 The layout and bathymetry of LA/LB port on mean tidal level (MTL) ….. 107
Figure 5.10 The incident wave for white noise analysis in LA/LB port ……………... 108
Figure 5.11 The predicted response at tidal station in LA/LB port (south source) ...... 109
Figure 5.12 The predicted response at tidal station in LA/LB port (west source) ….... 109
Figure 5.13 Spectra of oscillation in LA/LB port ……………………………………. 110
Figure 5.14 Amplification factor at tidal gauge with respect to kl …………..…...….. 111
Figure 5.15 (a) San Diego harbor on the West Coast; (b) & (c) Zoom-in …………… 112
Figure 5.16 The layout and bathymetry of San Diego harbor
on mean tidal level (MTL) ………………………………………..…….. 113
Figure 5.17 The incident wave for white noise analysis in San Diego harbor ………. 114
Figure 5.18 The predicted response at tidal station in
San Diego harbor (south source) ……………………………………….... 115
Figure 5.19 The predicted response at tidal station in
San Diego harbor (west source) ……………………………………….… 115
Figure 5.20 Spectra of oscillation in San Diego harbor …………………………….... 116
Figure 5.21 Amplification factor at tidal gauge with respect to kl …………..…...….. 117
Figure 5.22 (a) Pago Pago harbor in the South Pacific; (b) & (c) Zoom-in …………. 118
Figure 5.23 The layout and bathymetry of Pago Pago harbor on
mean tidal level (MTL) ……………………………………..………….. 119
Figure 5.24 The incident wave for white noise analysis in Pago Pago harbor ………. 120
Figure 5.25 The predicted response at tidal station in
Pago Pago harbor (south source) ……………………………………….. 121
Figure 5.26 The predicted response at tidal station in
Pago Pago harbor (east source) ………………………………………..... 121
Figure 5.27 Spectra of oscillation in Pago Pago harbor …………………………...…. 122
Figure 5.28 Amplification factor at tidal gauge with respect to kl ………..…………. 123
Figure 6.1 Water level without tidal effect in historical tsunamis ………………….... 126
Figure 6.2 Spectra of the corresponsive cases in Crescent City harbor ………….…... 127
xiv
Figure 6.3 Water level without tidal effect in historical tsunamis …………………… 128
Figure 6.4 Spectra of the corresponsive cases in LA/LB port ……………………..… 129
Figure 6.5 Water level without tidal effect in historical tsunamis ………………...…. 130
Figure 6.6 Spectra of the corresponsive cases in San Diego harbor …………….…… 131
Figure 6.7 The incident wave for white noise analysis in Crescent City harbor …….. 133
Figure 6.8 The layout and bathymetry of Crescent City harbor
on extremely low tide …………………………………………………...... 134
Figure 6.9 Predicted response at tidal station with extremely low tide (south source) 135
Figure 6.10 Predicted response at tidal station with extremely low tide (west source) 135
Figure 6.11 Spectral density of Crescent City harbor with extremely low tide ……… 135
Figure 6.12 The layout and bathymetry of Crescent City harbor on mean low water .. 136
Figure 6.13 Predicted response at tidal station with mean low water (south source) ... 137
Figure 6.14 Predicted response at tidal station with mean low water (west source) … 137
Figure 6.15 Spectral density of Crescent City harbor with mean low tide …………... 137
Figure 6.16 The layout and bathymetry of Crescent City harbor on
mean tidal level …………………………………………………………. 138
Figure 6.17 Predicted response at tidal station with mean tidal level (south source) ... 139
Figure 6.18 Predicted response at tidal station with mean tidal level (west source) .... 139
Figure 6.19 Spectral density of Crescent City harbor with mean tidal level ……….... 139
Figure 6.20 The layout and bathymetry of Crescent City harbor on
mean high water ……………………………………………………….... 140
Figure 6.21 Predicted response at tidal station with mean high water
(south source) ………………………………………...………………..… 141
Figure 6.22 Predicted response at tidal station with mean high water
(west source) …………………………………………………………….. 141
Figure 6.23 Spectral density of Crescent City harbor with mean high water ………... 141
Figure 6.24 The layout and bathymetry of Crescent City harbor on
extremely high tide ………………………………………………….….. 142
Figure 6.25 Predicted response at tidal station with extremely high tide
(south source) ………………………………………………………….... 143
xv
Figure 6.26 Predicted response at tidal station with extremely high tide
(west source) ……………………………………………………………. 143
Figure 6.27 Spectral density of Crescent City harbor with extremely high tide …...… 143
Figure 6.28 The sensitivity of Crescent City harbor on various tidal levels …….…… 144
Figure 6.29 Amplification factor at station with respect to kl
at low, mean & high tide ………………………………………………… 145
Figure 6.30 The incident wave for white noise analysis in LA/LB Port ………….…. 147
Figure 6.31 The layout and bathymetry of LA/LB port on extremely low tide …….... 148
Figure 6.32 Predicted response at tidal station
with extremely low tide (south source) …………………………………. 149
Figure 6.33 Predicted response at tidal station
with extremely low tide (west source) ……………………………….….. 149
Figure 6.34 Spectral density of LA/LB port with extremely low tide …………….…. 149
Figure 6.35 The layout and bathymetry of LA/LB port on mean low water ………… 150
Figure 6.36 Predicted response at tidal station with mean low water (south source) ... 151
Figure 6.37 Predicted response at tidal station with mean low water (west source) .... 151
Figure 6.38 Spectral density of LA/LB port with mean low water ………………….. 151
Figure 6.39 The layout and bathymetry of LA/LB port on mean tidal level ……….... 152
Figure 6.40 Predicted response at tidal station with mean tidal level (south source) ... 153
Figure 6.41 Predicted response at tidal station with mean tidal level (west source) .... 153
Figure 6.42 Spectral density of LA/LB port with mean tidal level ………………….. 153
Figure 6.43 The layout and bathymetry of LA/LB port on mean high water ………... 154
Figure 6.44 Predicted response at tidal station with mean high water (south source) .. 155
Figure 6.45 Predicted response at tidal station with mean high water (west source) ... 155
Figure 6.46 Spectral density of LA/LB port with mean high water ……………….… 155
Figure 6.47 The layout and bathymetry of LA/LB port on extremely high tide …….. 156
Figure 6.48 Predicted response at tidal station
with extremely high tide (south source) …...……………………………. 157
Figure 6.49 Predicted response at tidal station
with extremely high tide (west source) ………………………………..... 157
xvi
Figure 6.50 Spectral density of LA/LB port with extremely high tide …………….… 157
Figure 6.51 The sensitivity of LA/LB port on various tidal levels ………………...... 158
Figure 6.52 The incident wave for white noise analysis in San Diego harbor …….… 159
Figure 6.53 The layout and bathymetry of San Diego harbor on extremely low tide .. 160
Figure 6.54 Predicted response at tidal station
with extremely low tide (south source) ………………………………... 161
Figure 6.55 Predicted response at tidal station
with extremely low tide (west source) ………………………………….. 161
Figure 6.56 Spectral density of San Diego harbor with extremely low tide …………. 161
Figure 6.57 The layout and bathymetry of San Diego harbor on mean low water …... 162
Figure 6.58 Predicted response at tidal station with mean low water (south source) ... 163
Figure 6.59 Predicted response at tidal station with mean low water (west source) .... 163
Figure 6.60 Spectral density of San Diego harbor with mean low water ……………. 163
Figure 6.61 The layout and bathymetry of San Diego harbor on mean tidal level …... 164
Figure 6.62 Predicted response at tidal station with mean tidal level (south source) …165
Figure 6.63 Predicted response at tidal station with mean tidal level (west source) .... 165
Figure 6.64 Spectral density of San Diego harbor with mean tidal level ………….… 165
Figure 6.65 The layout and bathymetry of San Diego harbor on mean high water ….. 166
Figure 6.66 Predicted response at tidal station with mean high water (south source) .. 167
Figure 6.67 Predicted response at tidal station with mean high water (west source) ... 167
Figure 6.68 Spectral density of San Diego harbor with mean high water ………….... 167
Figure 6.69 The layout and bathymetry of San Diego harbor
on extremely high tide ………………………………………………….. 168
Figure 6.70 Predicted response at tidal station
with extremely high tide (south source) ………………………………... 169
Figure 6.71 Predicted response at tidal station
with extremely high tide (west source) ………………………………..... 169
Figure 6.72 Spectral density of San Diego harbor with extremely high tide ……...…. 169
Figure 6.73 The sensitivity of San Diego harbor on various tidal levels …………….. 170
xvii
Figure 6.74 Tide of Crescent City harbor based on water depth at station
(south source) …………………………………………………………… 171
Figure 6.75 Tide of Crescent City harbor based on water depth at station
(west source) ………………………………………………………….…. 172
Figure 6.76 Predicted response at tidal station starting from low tide ………………. 172
Figure 6.77 Predicted response at tidal station starting from high tide …………….... 173
Figure 6.78 Predicted response at tidal station starting from low tide ……………….. 173
Figure 6.79 Predicted response at tidal station starting from high tide …………...…. 173
Figure 6.80 Spectral density of south source scenarios in Crescent City harbor ….… 174
Figure 6.81 Spectral density of west source scenarios in Crescent City harbor ……... 174
Figure 6.82 Spectra comparison with Chile source (2010) in Crescent City harbor .... 175
Figure 6.83 Spectra comparison with Japan source (2011) in Crescent City harbor .... 175
Figure 6.84 (a) The spectral density distribution of tide gauge records with
tide filtered out at Crescent City harbor on normal day;
(b) The spectral density distribution of tide gauge records with
tide filtered out at Crescent City harbor on tsunami event …………..…. 176
Figure 6.85 Wave spectrum in May, June, July of 2008 at Crescent City Harbor ….... 177
Figure 6.88 Tide of LA/LB port based on water depth at station (south source) ……. 181
Figure 6.89 Tide of LA/LB port based on water depth at station (west source) ….…. 182
Figure 6.90 Predicted response at tidal station starting from low tide ………………. 182
Figure 6.91 Predicted response at tidal station starting from high tide ……………… 183
Figure 6.92 Predicted response at tidal station starting from low tide ……………….. 183
Figure 6.93 Predicted response at tidal station starting from high tide …………...…. 183
Figure 6.94 Spectral density of south source scenarios in LA/LB port …………..….. 184
Figure 6.95 Spectral density of west source scenarios in LA/LB port …………...….. 184
Figure 6.96 Spectra comparison with Chile source (2010) in LA/LB Port ……..…… 185
Figure 6.97 Spectra comparison with Japan source (2011) in LA/LB Port ………..… 186
Figure 6.98 Tide of San Diego harbor based on water depth at station (south source) 187
Figure 6.99 Tide of San Diego harbor based on water depth at station (west source) . 188
xviii
Figure 6.100 Predicted response at tidal station starting from low tide ……..………. 188
Figure 6.101 Predicted response at tidal station starting from high tide …………...... 189
Figure 6.102 Predicted response at tidal station starting from low tide ….………….. 189
Figure 6.103 Predicted response at tidal station starting from high tide …………..… 189
Figure 6.104 Spectral density of south source scenarios in San Diego harbor ............. 190
Figure 6.105 Spectral density of west source scenarios in San Diego harbor ……..…. 190
Figure 6.106 Spectra comparison with Chile source (2010) in San Diego harbor ...… 191
Figure 6.107 Spectra comparison with Japan source (2011) in San Diego harbor ...… 192
Figure 7.1 Tidal gauge records on 02/27/2010 in Crescent City Harbor ………….…. 195
Figure 7.2 Incident waves for Crescent City harbor …………………..……………... 195
Figure 7.3 Predicted response, solution by MOST and gauge record (48 hrs) ….…… 196
Figure 7.4 Predicted response, solution by MOST and gauge record (5 hrs) ………... 196
Figure 7.5 Comparison of spectral density distribution ……………………………… 197
Figure 7.6 Spectra comparison between gauge reading and incident wave …………. 197
Figure 7.7 Tidal gauge records on 02/27/2010 in LA/LB port …………...…….….… 198
Figure 7.8 Incident wave profile for Los Angeles/Long Beach port ………………… 198
Figure 7.9 Predicted response, solution by MOST and gauge record (48 hrs) ………. 199
Figure 7.10 Predicted response, solution by MOST and gauge record (5 hrs) ….…… 199
Figure 7.11 Comparison of spectral density distribution …………………………….. 200
Figure 7.12 Spectra comparison between gauge reading and incident wave …...….… 200
Figure 7.13 Tidal gauge records on 02/27/2010 in San Diego harbor ………….……. 201
Figure 7.14 Incident waves for San Diego harbor ……………………..………….…. 201
Figure 7.15 Predicted response, solution by MOST and gauge record (48 hrs) …...… 202
Figure 7.16 Predicted response, solution by MOST and gauge record (5 hrs) ……..... 202
Figure 7.17 Comparison of spectral density distribution ………………………..…… 203
Figure 7.18 Spectra comparison between gauge reading and incident wave …....…… 203
Figure 7.19 Tidal gauge records on 03/11/2011 in Crescent City Harbor ......…..…… 204
xix
Figure 7.20 Incident waves for Crescent City harbor ………………..….………..….. 204
Figure 7.21 Predicted response, solution by MOST and gauge record (48 hrs) …..…. 205
Figure 7.22 Predicted response, solution by MOST and gauge record (5 hrs) ……..... 205
Figure 7.23 Comparison of spectral density distribution …………………………….. 206
Figure 7.24 Predicted response, solution by MOST and gauge record (48 hrs) ……... 206
Figure 7.25 Predicted response, solution by MOST and gauge record (5 hrs) ……..... 207
Figure 7.26 Comparison of spectral density distribution …………………………….. 207
Figure 7.27 Spectra comparison between gauge reading and incident wave ………… 208
Figure 7.28 Tidal gauge records on 03/11/2011 in LA/LB port ………………….….. 209
Figure 7.29 Incident wave profile for LA/LB port …………………………..………. 209
Figure 7.30 Predicted response, solution by MOST and gauge record (48 hrs) …..…. 210
Figure 7.31 Predicted response, solution by MOST and gauge record (5 hrs) ………. 210
Figure 7.32 Comparison of spectral density distribution …………………………….. 211
Figure 7.33 Spectra comparison between gauge reading and incident wave ………… 211
Figure 7.34 Tidal gauge records on 03/11/2011 in San Diego harbor ………………. 212
Figure 7.35 Incident wave profile for San Diego harbor …………………………….. 212
Figure 7.36 Predicted response, solution by MOST and gauge record (48 hrs) ……... 213
Figure 7.37 Predicted response, solution by MOST and gauge record (5 hrs) ………. 213
Figure 7.38 Comparison of spectral density distribution …………………………….. 214
Figure 7.39 Spectra comparison between gauge reading and incident wave ………… 214
xx
ABSTRACT
Long waves may excite harbors to slosh intensively, and may severely damage the ship
mooring facilities and threatening lives, especially when wave period approaches to the
fundamental period of the harbor and the ship mooring system. Earlier studies of harbor
oscillation were largely focused on the resonance based on constant tidal level and the
resulting harbor layout. However, the tsunami events that occurred on Feb. 27
th
, 2010 and
Mar.11
th
, 2011 generated unusually more spikes in wave spectrum in the Crescent City
harbor, and in San Diego harbor. Earlier studies noticed this phenomenon, the present
study conducts specific frequency domain and time domain analysis to investigate the
reasons that lead to these spectral spikes in connection with resonant behavior of the
harbor basin.
The present study proceeds in 5 phases, which are model verification, study of harbor
oscillation based on constant mean tidal level, study of harbor oscillation based on five
separate tidal levels , study of harbor oscillation with continuously fluctuating tidal levels,
and simulation of historical tsunami events with realistic incident wave trains. Each phase
is explicated in details to determine the reasons that lead to the unusual resonant modes in
historical tsunamis.
One Boussinesq-type model is used and validated by laboratory experiments. This
model is used to predict response of harbors under impact of long incident waves in time
domain. Three major harbors in California and one harbor in American Samoa are
studied with white noise analysis on constant mean tidal level. The predicted responses at
tidal gauge station are transformed into spectra, which matches fairly with the primary
xxi
resonant mode simulated by mild slope equation in frequency domain simulation. The
present study compares the time domain analysis with the frequency domain analysis to
complement the understanding of harbor response.
The fundamental period is observed to be 22 minutes in Crescent City harbor, 60
minutes in Los Angeles/Long Beach harbor, and 273 minutes in San Diego harbor, based
on constant mean tide level. In some historical cases, however, the resonant periods are
not the same as earlier predicted. For example, Crescent City harbor shows multiple
spectral spikes in tsunami event on Feb. 27
th
, 2010 from Chile source and in tsunami
event on Mar. 11
th
, 2011 from Japan source. The fluctuating tidal level as well as the
corresponding change of harbor layout are two important reasons, whereas the energy
content of incoming waves also influence harbor oscillation. The present study takes state
of art process to consider the change of harbor layout due to the fluctuated tidal level, and
proves it as one of the reasons for some of the multiple spectral spikes. This phenomenon
is ascertained by tidal gauge records on normal days without tsunamis events.
The data from the tide gauge records are used in present study to validate numerical
model and to prove the hypothesis. The reasons of the multiple resonant modes in
Crescent City harbor, during the tsunami events of 2010 and 2011, are proved to be the
fluctuating tidal level with corresponding change of harbor layouts, and the fundamental
period for the larger region including continental shelf (72.5 min). The resonant mode of
Los Angeles harbor keeps fairly stable, and the topography of larger area outside the
harbor also influence the incoming waves. San Diego demonstrates different primary
resonant modes at different tide level, but the fundamental period for the larger sea area is
observed to be 58.5 min.
xxii
The present Boussinesq-type model is crosschecked with earlier study by mild slope
equation on constant tide level, and the agreement of both results indicate the nonlinear
effect in harbor oscillation does not appear to be significant. The movement of tidal level
will alter the fundamental period in harbors, through the changing bathymetry and the
associated layout of harbors. In Crescent City harbor, the tide level impacts response
intensity, and smaller water depth will cause response of larger amplification. In Los
Angeles/Long Beach port and San Diego harbor, the response amplitude remains stable
on different tide levels. White noise analysis with tide fluctuation demonstrates multiple
spectral spikes between 20 min and 25 min in Crescent City harbor, whereas the spikes of
lower frequencies are due to the fundamental period of larger sea area outside the harbor
as well as the energy content of the incoming waves. It has been noticed that the multiple
spectral spikes occur on normal days also, which means this phenomenon generally exists
in harbor oscillation. The spectra show larger energy magnitude on tsunami events than
on normal days. The simulation with MOST generated incident waves fairly matches
with the records by tide gauge station. Therefore, the combined effects of fluctuated tide
level, change of harbor layout, fundamental period of larger sea area outside harbor, and
the energy content of incoming waves all lead to the multiple spectral spikes on normal
days and on tsunami events.
1
CHAPTER 1: INTRODUCTION
1.1 Background
The word Tsunami is originated from Japanese language, meaning “waves in harbors”.
As a commonly seen natural disaster, tsunami is usually induced by a significant force
from underwater earthquake, volcano eruption or landslides on the border between plates.
The devastating waves contain large amount of energy, and is able to build up its height
as they propagate toward the coastal area. Tsunami can drown coastal region, threatening
people's life, and destroy structures, such as houses, bridges and vessels.
One of the most devastating tsunami happened on March 28
th
, 1964, following an
extremely powerful earthquake of magnitude 9.2 in the Prince William Sound region of
Alaska. In Crescent City of California, 11 people were killed and the business district was
destroyed by the deadly tsunami waves. In 2004, the Indian Ocean tsunami killed over
230,000 people in 14 countries along the coast of Indian Ocean, with waves as high as 30
meters (98ft) (Paris, Lavigne, and Sartohadi (2007)). In 2009, the tsunami generated by
Samoa earthquake killed over 189 people in the Pacific island countries, and severe
damage to the resident houses and harbors were reported. In 2010, Chile encountered the
attacks from a earthquake with magnitude 8.8. Tsunami was generated, causing
significant damage to several Chilean town along the Pacific coast. The economic loss
was estimated to be 15~30 billion US dollars, and 525 people were killed with another 25
people missing. About 9% of the local population lost homes in this disaster. In 2011,
Japan suffered from triple strikes of earthquake, tsunami, and nuclear disaster. The
tsunami was observed to reach up to 40.5 meters (133 ft) in Miyako and runup was as far
as 10
the F
break
detec
destro
in M
Calif
Figur
photo
Tsu
wave
avera
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speed
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ukushima D
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cted to be th
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of lives were
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speed of tsu
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Several tow
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3
depth is drastically reduced, thus, the wave speed decreased and the wave builds up its
amplitude (refraction). The propagating waves also scatter around offshore island,
breakwater, or other marine structure (diffraction). Once the wave hits the impermeable
boundaries, the waves are also bounced back (reflection). Based on the damaging modes,
the hazard of tsunami could be categorized as oscillation, current, inundation. These
hazardous phenomena sometimes occur simultaneously.
According to census in 2010, 39% of American people live in the counties directly on
coast, and most of important harbors are located on coast as well. The impact of tsunami
waves can threaten the life of millions and the well-being of the national economy. In this
way, it is necessary to study and understand the mechanism of this notorious natural
disaster. Therefore much research work has been conducted to focus on the tsunami
generation, tsunami travelling in the ocean, harbors oscillation in response to tsunamis.
4
1.2 Objective and Scope of Present Study
This study devotes much work to harbor oscillation in time domain. Once the frequency
of incident wave gets close to the fundamental frequency, the devastating fluctuation of
water surface will force vessels to smash onto the mooring system and break the mooring
cables as well. More severe damage will happen, if the resonance of mooring system is
triggered as well. These disasters can significantly threaten the secure operations of
harbors and maintenance of marine facilities. It is important that answer to the following
question be ascertained:
1. What are the fundamental frequencies of a given harbor basin?
2. Why are the spectral density distributions of some strong tsunami different
from the usual ones?
3. What are the possible reason that could change the resonance modes?
4. How much the nonlinear effect would take place in the harbor oscillation?
5. How much the dispersion would impact the harbor oscillation?
6. What role does the tidal level play in harbor oscillation?
7. How would the changing layout affect the fundamental frequency?
By conducting numerical analysis, we can find out the satisfying answers to these
questions. Meanwhile, we must keep in mind that the real world is much more complex
than numerical models, and there are always factors that are either technically impossible
to include or very difficult to simulate. Usually, one will often be trapped in a dilemma
between a better resolution and a better efficiency, and this would be up to the researcher
to determine the more important side of the problems.
5
The scope of the present study is listed as follow.
Chapter 2 presents the previous work about tsunami research, and the literature survey
generally focus on the harbor response in case of tsunami disaster. First of all, the history
of theoretical development in area of computational fluid dynamics is introduced. Then,
we review some successful research cases in the past, and their important conclusions are
emphasized to inspire the new research direction. Observation is very important for all
the studies, because it proves the theories through the truth and provides new problems to
research on.
Chapter 3 would mainly outline the methodology of this research and model construction.
Boussinesq-type model of finite difference scheme is introduced with its mathematical
formulation and discretization. Besides the boundary conditions and initial condition, the
issue of map projection is also specifically discussed.
In Chapter 4, the numerical model is validated through comparison with water basin
experiments by Lepelletier (1980). The setup of both physical and numerical models are
described, and six cases are investigated to verify the numerical model.
In Chapter 5, three harbors in California and one harbor in American Samoa are
simulated with white-noise analysis, and the results are compared with linear model and
field observations. The effect of nonlinearity and dispersion are studied based on mean
tidal level. One should notice that the tidal level in this chapter does not change as time
proceeds, which helps us to know the situation on constant bathymetry and harbor layout.
Chapter 6 and Chapter 7 solve the equation with tidal level fluctuating and with harbor
layout changing throughout one entire simulation process. Both real incident waves and
6
white noise incident waves are used as the incident wave train in the present numerical
model, in order to disclose the possible reason that makes the harbor oscillation different
from usual in Chile tsunami (Feb. 27
th
, 2010), and Tohoku tsunami (Mar. 11
th
, 2011).
In Chapter 5, the tidal level is maintained constant with time, whereas the tidal level in
Chapter 6 and Chapter 7 fluctuates to simulate the real tidal change. By doing so, the
contribution of tidal fluctuation in the harbor resonance is investigated.
7
CHAPTER 2: LITERATURE SURVEY
2.1 Theoretical Construction
To have a profound understanding of these phenomena of wave effects in coastal regions,
enormous amount of brilliant work has been done, in the past decades or even centuries,
to construct the theoretical basis of oscillation and current in scenario of various types of
incident waves. The theories can be categorized as in time domain and in frequency
domain. This section briefly reviews some important and widely used equations in
computational fluid dynamics.
The Helmholtz equation, named after German physicist Hermann von Helmholtz
(1821~1894), was introduced to provide a time-independent method to analyze
oscillation related phenomena. If the water depth is assumed constant and then the
velocity potential ϕ follow the Helmholtz equation:
22
2
22
0 (2.1) k
xy
To extend the application from constant water depth to variable water depth, Mild-Slope
Equation is used to incorporate the effect of wave refraction in harbor or bay. The mild-
slope equation was introduced by American physicist Carl Eckart (1902~1973) in 1952
and later improved to be a two-dimensional elliptic equation by Juri Berkholf in 1972.
This equation is currently widely in use of harbor oscillation research and can be written
as:
2
0 (2.2)
gg
CC k CC
8
The variable ϕ represents the horizontal variation in the velocity potential Ф,
where:
cosh ( )
{ ( , ) exp( )} (2.3)
cosh
kz h
Rxy it
kh
The variable ω is the circular wave frequency (2 π/T), the variable k is the wave number
(2π/L), the variable C is the wave celerity, and the variable C
g
is the group velocity.
The mild-slope equation is developed with depth-integrated procedure, meanwhile it
combined the effects of refraction and diffraction as well as the wave reflection from
basin boundaries.
In addition to frequency domain, it is also interesting to study the seiching in a harbor or
bay in time domain. The Navier-Stokes equations, named after French Engineer Claude-
Louis Navier (1785~1836) and British mathematician George Gabriel Stokes
(1819~1903), was originally derived from the application Newton's second law in fluid
motion. With the conservation of momentum described as the fundamental principle, the
general form of this equation is written as:
( ) (2.4)
v
vv P T f
t
With combination of conservation of mass, the Navier-Stokes equation is widely used in
the computational fluid dynamics. If the vertical length scale is assumed to be much
smaller than horizontal scale, it can be implicated based on the mass conservation that the
vertical velocity is negligible, comparing with horizontal velocity. This means the
vertical pressure gradient can be approximated as hydrostatic, and therefore the original
Navier-Stokes equation can be integrated along the depth dimension. This process
9
simplifies the equation by one dimension, and can be used to solve problem which does
not require detailed solution along vertical axis. Based on this point, the Shallow Water
Equation (Saint Venant Eq.) will be obtained, as the following expressions:
22
() ( )
0 (2.5)
() 1 ( )
( ) 0
2
uv
tx y
uuv
ug
tx y
22
(2.6)
() ( ) 1
( ) 0 (2.7)
2
vuv
vg
tx y
The equations above consider gravity as the only external force, with mass and
momentum conserved.
The Boussinesq equations are also widely used in fluid dynamics research, and it was
derived by French mathematician and physicist Joseph Valentin Boussinesq (1842~1929).
The equations are able to take frequency dispersion and weak non-linearity into account.
The Boussinesq-type equations are commonly used to simulate the oscillations in shallow
seas and harbors, and the equation can be expressed as:
22 2 222
22 2 2
3
( ) 0 (2.8)
23
h
gh gh
tx x h x
The main difference between the Shallow Water Equations and Boussinesq equation is
the dispersion effect. Many researchers adopt Boussinesq-type equations as the governing
equations, even though they are different from the original expression. The Boussinesq-
type equations all have similar characteristics, such as weakly nonlinear term and
10
dispersion terms. Sometimes, the velocity potential is used as the only unknown variables.
Wu (1979) published a Boussinesq-type equation as follow:
2
2
2
222
() [ ( ) ] {( ) }
26 63
[ ( )] [( ) ] ( , , , ) (2.9)
6
s
tt t tt tt tt
tt
r hh hh
hh hh
h
O
where: ߶ ത is the average velocity potential derived from depth-integrated procedure;
h is water depth; h
0
, l, H stands for a characteristic depth, length, and wave height;
α ,β, γ stands for nonlinearity, dispersion, and dissipation parameters.
To build a model with multiple unknown variables and more information, Boussinesq-
type equation is derived to solve the propagation of arbitrary long waves with moderate
amplitude over a mild bathymetry. Peregrine (1967) derived his version of Boussinesq-
type equation as follow:
33 3 3
2
22
[( ) ] [( ) ] 0 (2.10)
1( ) () 1
[ ] [ ] (2.11)
26
Du D v
tx y
uu u Du Dv u v
uv g D D
tx y x xt xyt xt xyt
v
33 3 3
2
22
1() ( ) 1
[ ] [ ] (2.12)
26
v v Dv Du v u
uv g D D
tx y y yt xyt yt xyt
where: ζ represents the surface elevation, D stands for the water depth. If the above sets
of equation are expressed in form of depth-integrated velocity (volume flux density), the
governing equations in the present study are acquired. See the methodology section of
Chapter 3 for more details.
11
2.2 Previous Research
The previous section lists some important theoretical achievements that virtually support
much research work in computational fluid dynamics. In this section, successful studies
are reviewed, and some of the important methods and conclusions are highlighted.
The early scientific study about free-surface oscillations in enclosed basin (e.g. lakes and
harbors) dated from 1800s, but the research more focused on tsunami, as the natural
disaster, started from 1950s. McNown (1952) and Kravtchenko (1955) used the Laplace
equation to conduct research on seiching tanks with circular and rectangular geometries,
based on theoretical and experimental analysis.
Miles and Munk (1961) incorporated the
effect of the wave radiating from the harbor open out to the external ocean, and then
investigated the wave oscillation in a rectangular harbor model. An integral equation in
term of a Green's function g(x,y, ξ) was found by Miles and Munk (1961) to satisfy the
Helmholtz equation inside the harbor with a presumed constant water depth. Ippen and
Goda (1963) proceeded the progress with more research on rectangular harbors
connected to the open sea, and the Fourier transformation method was used to evaluate
the wave radiation from the harbor entrance to the open sea. A fairly good match was
observed between theoretical and experimental solutions.
By this point, the arbitrary-shaped harbor oscillation was still an unsolved problem,
because the Green's function for arbitrary shape harbor was very difficult and complex to
obtain. Lee (1969) improved the study for an arbitrary-shaped harbor, with a better match
between theory and experiment. In Lee's work, a more effective wave-absorbing
boundary was adopted to make the laboratory condition more similar to the real open sea
12
condition. Lee (1969) originally developed a numerical method called "Boundary
Element Method", and this method was used to formulate an integral equation, in terms
of Green function, from the Helmholtz equation. Lee (1971) formulated the integral
equation for arbitrary shape harbors with constant depth, and solved it as matrix equation.
In the end, the solutions for outside and inside of the harbor entrance were matched. The
comparisons between the theoretical solution and experimental observation validated this
method. Lee and Xing (2008) studied the coastal response to incident wave using a finite
element model based on Mild-slope Equation. In this study, an arbitrary geometry and
variable depth were considered, and the effects of refraction, diffraction as well as
boundary absorption or reflection were included. The good match was reported between
the theoretical simulation and on-site observation, and the current velocity was also
estimated. In addition, this study also gave the suggestions on harbor reshaping
assessment and improvement.
In time domain, much important research was also conducted on long wave propagation
through the ocean, harbor oscillation, current and inundation on the coast. Lepelletier
(1980) applied Boussinesq-type equation into harbor oscillation with finite element
scheme, and the nonlinearity, dispersion, energy dissipation were taken into account.
Lepelletier and Raichlen (1987) applied this model in both experimental water basin and
real harbor.
Titov and Synolakis (1998, 2004, 2006) developed a numerical model “MOST” to
simulate the propagation across the ocean surface in global scale. Non-linear shallow-
water wave equations were adopted to govern the problem with finite difference scheme,
and the MOST model was built in spherical coordinate system with Coriolis force.
13
2.3 Observation and Analysis
The field observation is important and they aid the theoretical development. Observation
provides data for various kinds of analysis and is the basis for more advanced study,
therefore the research institutes and governmental organizations all over the world have
been dedicating resources, for decades, to collecting records about long wave phenomena.
Some of the data are obtained from instruments in the field, whereas the others come
from laboratory work. The idea is to generalize some pattern out of the "random"
behavior of oscillations or current in a given water body, through analysis of
experimental data and modeling. Once these analysis and models are verified with
observation, we will have a better understanding of the relevant problems and predict the
possible outcomes, based on the knowledge, to give guidance for the practical work in
bays and harbors.
The National Oceanic and Atmospheric Administration (NOAA) in the United States
Department of Commerce serves the public with weather forecasts, natural disaster
warning, global climate monitoring and coastal restoration. This agency has devoted over
four decades to collecting oceanic and meteorological data to protect the national security.
Rabinovich and Leviant (1992) studied the influence of seich oscillation on long
wave spectra. They selected three locations, including one strait and two bays, in South
Kuril-islands to investigate the oscillation under impact of long waves with historically
stable periods and spectra. The Eigen mode of each location was inspected and there was
good match between observation and theoretical computations of seiches for the given
basins. Each location has its dominant seich mode.
Ev
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19.5 m, and
heights and
enote inund
erall east Jap
fundamental
g wave.
was also co
ue of Light
a Bay, based
11 m/s wa
bore. Mori,
apanese east
the longest i
d inundation
ation height
pan, and (b) i
l mode of th
onducted fo
Detection a
d on videos
as observed
et. al (2011)
t coast, inclu
inundation d
n heights alo
ts, and the b
is for the Se
he harbor wa
or the Tohok
and Ranging
s taken by s
in the Kese
) surveyed th
uding 5300 l
distant reach
ong the east
blue color d
endai region.
16
as 16 minute
ku tsunami o
g (LiDAR) t
survivor. Th
ennuma Bay
he inundatio
locations. Th
hed 5 km.
t Japan coas
denotes runu
es
of
to
he
y,
on
he
st.
up
Figur
View
re 2.3 The o
w (a) is overa
observed inu
all Japan, and
undation hei
d View (b) i
ght and run-
s above Seid
-up height a
dai. (Source:
along east Ja
: Mori, et. al
17
apanese coas
l (2011))
st.
18
CHAPER 3: MOTHEDOLOGY AND MODEL
Lee and Xing (2008) , based on mild-slope equation, studied resonance in Californian
and Asian harbors, and their simulation matches with observation by local tidal gauges.
Given that their model is linear and in steady state (frequency domain), it would be
interesting to adopt a nonlinear, dispersive model in transient state (time domain) to
ascertain and complement the earlier work as the preliminary step of present study.
In this chapter, the governing equations supporting the study of harbor oscillation
problem in time domain are concisely introduced. Then, boundary conditions are
described, as well as the initial conditions. Later on, pretreatment and discretization
scheme are explained to transform the original governing equations into computer
friendly difference equations. After that, ADI algorithm and Double Sweep algorithm are
introduced to solve the resulting numerical system. Collecting the correct cartographic
data requires much careful preparation, and the specific details are given in the relevant
section of this chapter. Last but not least, the method to acquire bathymetry and incident
wave is discussed. For the present study the computer program MIKE21bw is utilized for
numerical computations. The work by Madsen, Sorensen and Schaffer in 1991~1998 are
cited as reference.
19
3.1 Governing Equation
In the present study, one set of Boussinesq-type equations derived by Peregrine (1967)
are adopted as the governing equations:
00
33 33
2 00
00 22
[( ) ] [( ) ] 0 (3.1)
() ( ) 11
[ ] [ ]
26
hu h v
tx y
hu h v uu u u v
uv g h h
tx y x xt xyt xt xyt
33 33
2 00
00 22
(3.2)
() ( ) 11
[ ] [ ] (3.3)
26
hv hu vv v v u
uv g h h
tx y y yt xyt yt xyt
where: η is water surface elevation,
h
0
is water depth at still,
g is gravity acceleration,
u, v represent velocity component in x and y direction, respectively.
The set of governing equations above consists of two essential parts, including continuity
(3.1) and momentum equations (3.2) (3.3). Unlike linear theories, the Boussinesq type
equations retain the high order terms through truncation, and this would make the model
containing terms representing nonlinearity and dispersion. The governing equations are
essentially equivalent as the other nonlinear theories in time domain, meanwhile, the
present model is well developed in terms of convenience of operation. For instance, the
bathymetric map is directly edited as spreadsheet, which is very straightforward and can
be easily visualized. As for the boundary conditions and incident waves, the present
model has advanced function tools to efficiently generate data files
.
20
If the velocity components u and v are taken as depth-integrated velocity, equations (3.1),
(3.2), and (3.3) can be rewritten as follows (Abbott (1978)):
233
00
0 2
0 (3.4)
1
( ) ( ) [ ( ) ( )]
2
PQ
tx y
hP hQ PP PQ
gh h h
txh y h x xt h xyt h
33
2
0 2
233
00
0 2
(3.5)
1
[ ( ) ( )]
6
1
( ) ( ) [ ( ) ( )]
2
PQ
hh
xt h xyt h
hQ h P QQ PQ
gh h h
tyh x h y yt h xyt h
33
2
0 2
(3.6)
1
[ ( ) ( )]
6
QP
hh
yt h xyt h
where: η is water surface elevation,
h
0
is water depth at still,
h is the total water surface elevation (h=h
0
+η),
P is the volume flux density in x direction (P=uh),
Q is the volume flux density in y direction (Q=vh).
.
The equations (3.4)~(3.6) are further simplified as follow (Abbott (1978)):
2
2
0
0 (3.7)
1
( ) ( ) ( ) 0
3
tx y
tx y x xxt xyt
PQ
PPQ
PghhPQ
hh
2
2
0
(3.8)
1
( ) ( ) ( ) 0 (3.9)
3
t y x y yyt xyt
QPQ
QghhQP
hh
In Section 3.3 ~ 3.5, method of pretreatment, dicretization, and solution are exhibited.
3.2 B
The s
Figur
Ba
liquid
progr
Boundary C
sketch of an
re 3.1 The s
ased on the
d, which rep
ram recogniz
y
x
Coas
Conditions a
arbitrary sha
ketch of an a
character (p
present sea a
zes the area
tline
and Initial C
ape geometr
arbitrary sha
phase), the s
and land. By
as inactive
Sea
(Outsid
Sea W
(Inside H
Condition
ry is shown a
ape harbor g
simulation d
y marking th
domain, and
Absorbing
Water
de Harbor)
Water
Harbor)
Incident
as below:
eometry
domains are
he characteri
d the simula
g Boundary
L
t Wave
categorized
istic number
ation result h
Land
21
d as solid an
r on land, th
hence is void
nd
he
d.
22
If any value other than the marker numbers is assigned to the sea, the numerical system
recognizes this area as active domain, and simulation result hence is valid. The assigned
number is taken as local seabed (or ground) elevation. Now, the definition of simulation
domains leads to two types of boundaries, including the absorbing boundary to the far
field and the coastline boundary to the land.
(1). Absorbing Boundary
The waves radiating out to the far field ocean never come back to the harbor. When
traveling out to the far field, the radiated waves are absorbed numerically to imitate the
natural process. Larsen and Dancy (1983) provided formula to construct a set of “sponge
lines”, which eliminates the radiated waves and flows. As the waves travelling across
each sponge line, the surface elevation and flow are divided by a set of numbers.
Larsen and Dancy (1983) defined the function of division number as follow:
/ /
exp[(2 2 )ln ] for 0 x x
( ) (3.10)
xx xx
s
s
a
x
1 for x
s
x
where: μ is the division number, x is location variable, x
s
is the total thickness of the
sponge layer, △x is the distance between two neighboring sponge lines, a is a constant
number that is determined by the number of grid lines in the sponge layer.
These division numbers increase as the wave approach the outer lines of the sponge
layer, and the whole process repeats at each time step. The effect of absorbing boundary
is magnified as time proceeds and waves move across.
{
23
(2). Reflective Boundary and Energy Loss
As waves reach the solid boundary, they are partially reflected. Due to the laminar or
turbulent friction caused by porosity of structures, some energy is dissipated as well.
Madsen (1983) provided an analytical solution to model reflection coefficient for linear
short waves, and it reads:
2
2
||
| | (3.11) /
1(1 )
1(1 )
R ri
iw
iw
aa
e
e
where:
1
n
if
, and 1
w
if
gh
α
R
is the reflection coefficient,
a
i
is the incoming wave amplitude, a
r
is the reflected wave amplitude,
n is the porosity of the structure, w is the thickness of the structure,
f is a friction factor which is assumed to be independent of x and t.
However, this solution has limitation. The flow resistance is linearized in the porous
boundary, and the friction factor is obtained in an implicit form by using Lorentz’
principle of equivalent work. Even though this analytical solution works well in ideal
condition of linear and regular waves, this model needs to be combined with some
assumption in real practice. In the present study, the porosity values are assumed within
reasonable range, and different sections of the coastlines are assigned with different
porosity values, based on the texture and width of the structures.
(3). Initial Condition
All the initial surface elevations and velocities are assumed to be zero at the beginning.
24
3.3 Pretreatment and Discretization
To take nonlinear convection into account, Madsen and Sorensen (1992) rewrite the
nonlinear terms in the original governing equations (3.7)~(3.9), which read:
2
32
00
00
0 (3.12)
11
( ) ( ) [( ) ( ) ] ( ) 0
62
tx y
t x y x xxt xyt xxt xyt
PQ
PPQ P Q
Pghh hPQ
hh h h
2
32
00
00
(3.13)
11
( ) ( ) [( ) ( ) ] ( ) 0 (3.14)
62
t y x y yyt xyt yyt xyt
QPQ Q P
Qghh hQP
hh hh
The spatial derivative of water depth is included, and the difference between the water
depth at still and total water depth are neglected. To generalize Boussinesq type equations
and to represent corresponsive linear dispersion relations, the governing equations are
transformed, through linear long wave approximation, into the following expressions
(Madsen and Sorensen (1992)):
2
23
00
00
0 (3.15)
1
() ( ) ( ) ( ) ( )
3
11
()(
36
tx y
t x y x xxt xyt xxx xyy
xxt
PQ
PPQ
PghBhPQBgh
hh
hh P
00 00 0
2
23
00
00 0 0 00 0
1
2 ) ( ) ( ) 0 (3.16)
6
1
() ( ) ( ) ( ) ( )
3
11 1
( ) ( 2 ) ( ) ( ) 0
36 6
yt xx yy y xt xy
t y x y yyt xyt yyy xxy
yyt xt yy xx x yt xy
QBgh Bgh hh Q Bgh
QPQ
QghBhQPBgh
hh
hh Q P Bgh Bgh hh P Bgh
(3.17)
where: B is an arbitrary constant.
The c
Stoke
very
h/L
0
r
In Se
in det
3
The
(3.15
hyper
equat
constant B is
es first order
well, and th
reaches up to
ection 3.3.1 a
tail, and Figu
Figure
.3.1 ADI sc
Alternative
), (3.16), an
rbolic and e
tions into tw
s determined
r theory. Ma
he resulting
o 0.5 (deep w
and 3.3.2, th
ure 3.2 illust
e 3.2 A typic
cheme
Direction I
nd (3.17). Th
elliptic partia
wo sweeps in
d by calibrati
adsen and So
error was on
water limit).
he discretizat
trates a typic
cal CV and t
Implicit (AD
his finite diff
al differentia
forms of de
ing the cons
orensen (199
nly 4% from
tion scheme
cal 2D Carte
the notation
DI) scheme
ference schem
al equations
erivatives in
equent linea
92) noticed
m the Stokes
and solving
esian grid str
used for Car
is used to
me is widely
s, and it wou
x and y dire
ar dispersion
that value B
s first order
g algorithm a
ructure.
rtesian 2D g
discretize t
y used to sol
uld split fin
ection.
25
n relation wit
B=1/15 work
theory, whe
are introduce
grid
the equation
lve parabolic
ite differenc
th
ks
en
ed
ns
c,
ce
26
(1). x-sweep equations (Madsen and Sorensen (1992)):
1/2
11/21/2
12
1/2 1/2 * 1/2
2
1 0
11
( ) ( ) ( ) 0 (3.18)
1
22
2
( ) ( ) ( )
13
( ) [( ) (
32
nn
nn n n
xx y y
nn
nn n
xy x
nn
xx xx
PP Q Q
t
PP P PQ
gh
th h
h
BPP
t
1/2 1/2 1/2 3/2
1 1/2 1/2 1/2 3/2 00
00 1/2 1/2 1/2 3/2
2*
00
1
)( )]
2
()11 1
[ ( ) ( ) ( )]
34 12
()
11
[ ( ) ( )]
412
[ (
nn n n
xy xy xy xy
nn n n n n x
xx y y y y
y nn n n
xx x x
xxx xyy
QQ Q Q
hh
PP Q Q Q Q
t
hh
QQ QQ
t
Bgh h
*** *
00
) ( ) (2 ) ( ) ] 0 (3.19)
xxx yy yxy
hh
where η
n+1/2
and P
n+1
are unknown variables.
(2). y-sweep equations (Madsen and Sorensen (1992)):
11/2
13/21/2
3/2 1/2 2
11 **1
2
3/2 0
11
( ) ( ) ( ) 0 (3.20)
1
22
2
( ) ( ) ( )
() 1
( ) [(
3
nn
nn n n
xx y y
nn
nn n
yx y
nn
yy yy
PP Q Q
t
QQ Q PQ
gh
th h
h
BQQ
t
1/2 1 1
00 3/2 1/2 1 1
11 00
2** ** **
00 0
31
)( ) ( )]
22
()
11 1
[ ( ) ( ) ( )]
34 12
()11
[ ( ) ( )]
412
( ) [ ( ) ( ) (2
nn n n
xy xy xy xy
y nn n n n n
yy x x x x
nn n n x
yy y y
yyy yxx y yy
PP P P
hh
QQ P P PP
t
hh
PP P P
t
Bg h h h
** **
0
) ( ) ] 0 (3.21)
xx x xy
h
where η
n+1
and Q
n+3/2
are unknown variables, the superscript* and ** denote the values at
time level n+1/2 and n+1, which is obtained from explicit use of the continuity equation.
27
The x and y derivatives are remained as differential express to simplify the appearance
and emphasize the time-centering approximation. The spatial derivatives of linear terms
are taken as straightforward mid-centering approximation, and the nonlinear convective
terms are treated with “side-feeding” (Madsen and Sorensen (1992)).
3.3.2 Solving method
After discretizing the differential equation, a tri-diagonal system is obtained and finally
solved by the Double Sweep algorithm. In the present model, the entire solving procedure
is realized in the following steps (Madsen and Sorensen (1992)):
1. Set the boundary conditions and initial condition.
2. Compute η
n+1/2
, and η
n+1
explicitly through continuity equations.
3. Compute η
xxx
, η
xyy
, η
yyy
, η
yxx
, η
xx
, η
yy
, and η
xy
.
4. Time-center the nonlinear gravity and convective terms with side-feeding technique.
5. Acquire a tri-diagonal matrix system, and solve it with Double Sweep algorithm.
6. Acquire P
n+1
, and Q
n+3/2
.
7. Repeat Step 2~6 for the next time step.
The steps above have three advantages:
i. For the n×n tri-diagonal matrix system, the Double Sweep algorithm is able to
solve it in O(n) actions, whereas Gaussian elimination takes O(n
3
) actions.
ii. By computing η
n+1/2
, and η
n+1
explicitly, the nonlinear gravity and convective
terms are linearized by the side-feeding technique, which saves the trouble of
iteration.
iii. The slope and curvature of water surface are available on each time step, which
provides more information.
28
3.4 Mapping Projection and Bathymetry
The present study models several real harbors, and their layouts are important input data
for the computation. This section introduces the method how to search for the map data,
how to transform the data of GPS coordinates into the usable format in 2D plane, how to
choose the map size, and how to choose the spatial resolution.
As widely known, the Earth is an irregularly spherical object, therefore spatial concept in
reality conflicts with people’s intuition. For example, if one travels in a straight line on
surface of the Earth for a long distance, the travelling path ends up to be a curve from the
Space view. If we take a look at the projected global map in the 2D plane, the shortest
route between two locations on different meridians is not the straight line. Hence, one
cannot simply draw a straight line on a 2D global map to claim it to be the shortest route,
which instead needs careful translation between 3D polar coordinate system and 2D
orthogonal coordinate system.
The essential reason of this anti-intuition problem is the ignorance of the curvature of the
land surface, which is a mistake based on life experience of the earlier human history.
During the period before industrialization, the advanced technique of global travelling or
cartographic surveying was out of touch, and the transportation was relying on the animal
power. The severely low productivity limited the activity area of human into some small
regions, and the land shape seems to be “flat” from the local view on a spot of the Earth.
Ever since the renaissance, people started to doubt this idea under impact of ancient
Greek philosophy and natural science. The correct spatial concept was proved during the
Age of Discovery, and has completely established with the development of industrialized
trave
of the
prefe
vario
surfa
some
on. N
proje
the ri
Figur
lling techno
e most impo
r to think ab
us techniqu
ce into a pla
e chosen info
Nevertheless
ction, which
ight method
re 3.3 The c
logy. The tr
ortant achiev
bout problem
es of projec
ane surface.
ormation rem
, none of th
h makes mis
of mapping
chart of Cres
ruth of the E
vements of g
ms on a plane
ction has bee
Different pr
mained, such
hese theories
sshape inevi
projection.
cent City ha
Earth shape i
eography, ho
e in subcons
en develope
rinciples def
h as area of u
s remain all
itable. There
arbor (CA) b
is widely kn
owever, peo
scious. In ord
ed to map th
fine differen
unit block, l
the correct
efore, it is v
before projec
nown and acc
ople nowaday
der to satisfy
he locations
nt rules to tra
length of uni
information
very importa
ction
29
cepted as on
ys would sti
y this deman
on the Eart
ansform, wit
it line, and s
n through th
ant to choos
ne
ill
nd,
th
th
so
he
se
T
Comp
comp
Atmo
one c
spots
N
map,
the ax
Figur
The d
to be
but ap
After
The present s
pany, which
pared with t
ospheric Adm
chart before
mark the se
Normal Merc
and the prin
xis of the Ea
re 3.4 A typ
distortion is
much large
ppears to be
r the projecti
study adopte
h provides th
the ones fro
ministration
projection
eabed elevati
cator project
nciple is to u
arth. The Fig
pical process
insignifican
er than the re
e over 2 time
ion, all the m
ed the map
he navigation
om Office o
(NOAA), t
in GPS coo
ion value an
tion is used
unfold the E
gure 3.4 dem
of normal M
nt at low lati
eal size. For
es larger than
meridian bec
data from J
nal chart ser
of Coastal S
o make sure
ordinates (Lo
d the circle s
d to transfor
Earth surface
monstrates a t
Mercator pro
itude, but the
example, G
n Australia o
comes paral
Jepessen, a
rvices. This
Survey in th
e its accurac
ongitude, La
spots denote
rm the origin
e onto a cyli
typical proce
ojection (Sou
e area at hig
Greenland is
on the Merca
llel to each o
subsidiary o
navigational
he National
cy. The Figu
atitude), wh
e the coastlin
nal chart in
inder with ax
ess of projec
urce: USGS)
gh latitude w
not as large
ator projecte
other, other
30
of the Boein
l chart is als
Oceanic an
ure 3.3 show
here the cros
ne.
nto usable 2D
xis parallel t
ction.
)
would appear
e as Australia
ed global ma
than crossin
ng
so
nd
ws
ss
D
to
rs
a,
ap.
ng
at the
there
of Cr
Figur
In or
reaso
up th
of nu
time
limit
e polar poin
fore the erro
rescent City
re 3.5 The m
der to simul
onable area o
he sponge lay
umerical simu
step Δt and
value for Cr
nts. In the p
or caused by
after project
map of Cresc
late oscillati
of the sea ou
yer and to pr
ulation, Cou
spatial reso
r is set to be
present stud
y projection
tion.
cent City har
ion, the enti
utside the ha
ropagate the
urant number
olution Δx. T
1 in the pre
dy, all the h
is very smal
rbor (CA) af
ire harbor is
arbor. The se
waves into
r
t
Cr c
x
The variable
sent study.
harbors are
ll. The Figu
fter projectio
s included in
ea area shou
the harbor. T
is calculated
e c stands fo
in the low-
ure 3.5 illustr
on
n the map, a
uld be large
To guarante
d beforehand
or the celerit
31
-latitude area
rates the ma
as well as th
enough to se
e the stabilit
d to adjust th
ty. The uppe
a,
ap
he
et
ty
he
er
32
3.5 Incident Wave
Two types of incident waves are used for different purposes, including Cnoidal wave in
the experimental validation and irregular waves in the real harbor computation. For each
incident waves, there are four relevant factors that contributes to the simulation, and they
are surface elevation, slope of surface elevation, curvature of surface elevation, and flux
density. The 1
st
order Cnoidal wave theory is used to provide the necessary information,
Wiegel (1960) gives following formula:
1. Wavelength:
3
16
L=kK(k) (3.22)
3
d
H
where:
2
(/ ) ( / )
21( /)
(2 1 ) ( ) (2 2 ) ( )
ct
t
tct
yd y d
k
Lyd
yyy
LEk L Kk
ddd
2. Celerity:
2
1()
{ 1 [ 1 (2 3 )]} (3.23)
()
HEk
Cgd
dk Kk
3. Wave profile:
2
[2 ( )( ), ] (3.24)
st
xt
yy Hcn Kk k
L T
where: T=L/C
33
4. Fluid partial velocities
222
22
23
23
[ ( ) ] (3.25)
432
11
[( ) ( ) ]
23 2
uh h d y h
dd d x gd
vhh yh
yd
ddx d x gd
2
(3.26)
cn [2 ( )( ), ] (3.27)
t s
xt
hy d d y H Kk k
LT
where: y
c
and y
t
are the distances from bottom to the crest and trough, respectively.
d is the still water depth, g is gravity acceleration, H is the maximum wave height.
x and y are coordinates, u and v are the velocity components in x and y direction.
K(k) is the complete elliptic integral of the first kind with modulus k.
E(k) is the complete elliptic integral of the second kind with modulus k.
For oscillation in the real harbors, irregular waves are introduced to imitate either ideal or
historical conditions. White noise analysis identifies fundamental frequency of harbors,
and this method is used in the earlier study by Gierlevsen et. al (2001) and Kofoed-
Hansen et. al (2005). The principle is to stimulate the harbor with an idealized wave
trains that cover certain frequency range with equal energy, which cannot be used to
represent the historical oscillation. In order to fulfill this work, some realistic wave
profiles have to be adopted, and the MOST model developed by Titov and Synolakis
(1998, 2004, 2006) provides such an option. By extracting the propagated wave from the
MOST model, the historical harbor oscillation can be investigated with more meaning in
reality.
34
CHAPTER 4: MODEL VERIFICATION
In this Chapter, the present model is verified through the comparison between the results
of simulation and experiment.
As the beginning, the configuration of experimental device is illustrated, and the result
by Lepelletier (1980) is presented as the reference. The experiment is based on direct
observations from the oscillation basin, and it provides reliable data for comparison with
numerical simulation results. Besides, the setup of numerical model, including
computation power, choice of mesh size and time step, boundary conditions, and
convergence are all explained with details. Study is mainly focused on the oscillation in
transient state and uses the experimental result of earlier study to validate the present
model. There are four factors that are involved in the models, including harbor shape,
harbor size, bathymetry, and category of incident wave. These factors have different
combinations in each experimental case, which come up with six setups of simplified
harbor model in the experiments. Each of the setup is treated as one case in this chapter,
and the same conditions are used in the numerical model to compute the predicted
response in transient state. With both numerical solution and experimental data in hand,
the numerical model is validated through comparison.
In the experiments, a probe gage was installed in the middle of the deep inside backwall
to measure the water surface. Therefore, the numerical solution at the probe gage location
is used for comparison analysis. In the later sections, the probe gage location is marked
by a star, and the incident wave generation boundary is marked with a yellow line.
4.1 E
Fig 4
meas
was c
Experiment
4.1~Fig 4.4
urement dev
conducted in
Figure
Figure
al Setup
show the
vices in the
n a wave bas
e 4.1 Overal
e 4.2 The w
water basin
experiment
in with 9.60
l view of the
wave generato
n, wave gen
t by Lepelle
0 m × 4.73 m
e water basin
or (Source: L
nerator, harb
etier (1980).
m (31.5 ft × 1
n (Source: L
Lepelletier (
bor model a
. The experi
15.5 ft).
Lepelletier (1
(1980))
35
and respons
imental wor
1980))
se
rk
Alon
the op
Figure
Figure
g the sidewa
pen sea cond
4.3 A rectan
4.4 (a) The
(b) Prob
alks of the w
dition (i.e. w
ngular harbo
integrated s
be to measur
wave basin,
waves radiate
or model (So
system to con
re surface ele
layers of w
ed from the h
ource: Lepel
ntrol, receiv
evation (Sou
wave absorbe
harbor entran
(a)
lletier (1980)
ve, and monit
urce: Lepelle
ers are place
nce die out a
36
))
tor signal
etier (1980))
ed to simulat
at infinity).
(b)
te
37
4.2 Numerical Model Setup
4.2.1 Computation Power
The numerical model is very efficient, and it takes regular computation power to finish
the work. One set of Pavilion Magnesium PC, manufactured by HP, is used to conduct
the simulations, and the make is Gray Edition p6774y. Table 4.1 shows the parameters
and setups of the computer used in present study.
Table 4.1 The configuration of computation power in the present study
Category Content
CPU AMD Phenom
TM
II 840 T Quad-Core Processor
System memory 6GB DDR3
Hard Drive 1 terabyte
DVD Burner SuperMulti DVD Burner with Light Scribe Technology
Integrated Graphics ATI Radeon
TM
HD 4200
Wireless LAN 802.11b/g/n
Operation System Genuine Windows
R
7 Home Premium
With appropriate definition of resolution and time step, the simulations in the present
model takes acceptable time length to run. At the peak of computation activity, the usage
of RAM goes up to 90%. For validation, one run takes approximately 2 minutes, and each
project takes 110 MB~180 MB in the hard drive. To simulate the oscillation in harbors,
one run takes 2hr~10hr, based on different harbor sizes, and each project takes 1 GB~2.8
GB in the hard drive.
38
4.2.2 Choice of Resolution and Time Step
Proper resolution and time step have to be determined to fit the numerical model into the
reality as much as possible and to guarantee an efficient usage of computation resources.
The reasonable choice pursues the optimized point through the tradeoff between the two
sides. Table 4.2 demonstrates the resolution and time step in the validation part and real
harbor part.
Table 4.2 The resolution and time step for water basin and real harbor
Model Resolution Time Step
Water Basin (Experiment) Δx Δy Δt
Case 1 5 mm 5mm 4 ms
Case 2 5 mm 5mm 4 ms
Case 3 5 mm 5mm 4 ms
Case 4 5 mm 5mm 4 ms
Case 5 5 mm 5mm 4 ms
Case 6 5 mm 5mm 4 ms
Real Harbor (Application) Δx Δy Δt
Crescent City,
CA
9 m 9 m 0.4 s
Los Angeles/Long Beach,
CA
20 m 20 m 0.8 s
San Diego,
CA
40 m 40 m 1.2 s
Pago Pago,
American Samoa
10 m 10 m 0.5 s
4
The b
which
the la
The w
water
block
4.2.3 Choice
boundary con
h involve sp
ayout of a typ
Figure 4
white part r
r area. As ca
ked entrance
e of Bounda
nditions of v
ponge layer
pical harbor
4.5 The dist
epresents la
an be seen, t
. The exterio
ary Conditio
validation ex
and fully ref
r model in th
tribution of s
and (solid ph
the harbor is
or boundary
ons
xperiments a
flected boun
he water basi
sponge layer
hase) in the
the trapezo
marked by a
are much sim
ndary only. T
in.
r coefficient
model, and
idal and nar
a rainbow co
mpler than th
The Figure 4
d the blue pa
rrow wedge
olored band
39
he real harbo
4.5 illustrate
art stands fo
with partiall
demonstrate
or,
es
or
ly
es
the sp
exper
defin
ponge layer
riment, the w
ned to be 100
Figure
, and the leg
walls are im
0% along the
4.6 The full
gend exhibit
mpermeable,
e coastline as
ly reflective
ts division n
vertical and
s red color m
boundary
number μ in
d smooth, th
marked in the
n the sponge
herefore the
e Figure 4.6
40
e layer. In th
e reflection
.
he
is
4
Besid
impo
spong
separ
The s
amou
4.2.4 Intern
des the boun
rtant elemen
ge layer is t
rately. The F
Figure 4
sponge layer
unt of compu
nal Wave Ge
ndary condit
nt in the num
hat the mod
Figure 4.7 sh
4.7 Internal
r simply nee
utation resou
eneration L
tions, the me
merical mode
del system c
hows the loca
wave gener
ds to absorb
urces and tim
Line
ethod to init
el. The adva
an process t
ation of inter
ation line
b the waves t
me.
tiate the wav
antage of gen
the radiated
rnal wave ge
travelling ac
ve propagati
nerating wav
wave and i
eneration lin
cross, and th
41
ion is anothe
ves inside th
ncident wav
ne.
his saves quit
er
he
ve
te
42
4.3 Group A: Rectangular Harbor
Group A has 4 cases all together, and their common place is that the harbor models are
rectangular. The length and width ratio is 5:1 for all the rectangular harbors, and the
gauge probe is installed in the middle of the back wall at deep end of the harbor models.
There are three variable factors, including incident wave category, entrance blockage, and
water bottom profile. The incident waves can be divided as periodical wave and damping
transient wave; The entrance blockage is quantified with the percentage of opening width;
The water bottom profile is observed to be either constant water bottom (flat) or linearly
decreasing (rising up) along the longitudinal direction of the harbor model. These three
factors are organized with different combinations, and setup of the 4 cases are
specifically described in Table 4.3.
Table 4.3 The variable factors of harbor models in Group A
Content Case 1 Case 2 Case 3 Case 4
Incident Wave periodical periodical transient transient
Entrance 100% open ≤ 100% open 100% open 100% open
Water Bottom constant constant constant
linearly
changing
Besides setups above, the incident wave amplitude or (and) harbor size controls the
individual experiments in each case, and they are explicated in the subsections.
4
Case
Table
botto
indic
The T
Table
Mo
1
2
3
4
4.3.1 Case #
#1 has rect
e 4.3, the in
m is be uni
ates gauge p
Table.4.4 exh
e 4.4 Dimen
del
In
W
1 Fi
2 Fi
3 Fi
4 Fi
#1
tangular har
ncident wave
iformly flat.
probe.
Figure 4.
hibits the sp
nsions of the
ncident
Wave
ig. 4.9
ig. 4.9
ig. 4.9
ig. 4.9
rbor model w
e is periodic
. The harbor
8 A typical
ecific dimen
e harbor mod
a (cm)
2.8
6.0
10.2
13.2
with ratio o
cal, the entra
r model is s
plan view o
nsions of the
dels in Case #
l (cm)
14.0
30.0
51.0
66.0
of length to
ance would
sketched in
of the harbor
e harbor mod
#1
h (cm)
6
6
6
6
width 5:1.
be fully ope
Figure 4.8,
r in case 1
dels in Case
) T (s
1.9
1.9
1.9
1.9
43
As shown i
en, and wate
, and the sta
#1.
s)
9
9
9
9
in
er
ar
The h
depth
all th
Fig
This
the i
gener
the e
condi
dissip
gener
incid
gener
the in
the ou
harbor size i
h and inciden
e 4 models o
gure 4.9 Inci
wave profil
incident wav
rated by a p
entrance of h
itions, the w
pation. Ther
rator. The n
ent wave fil
ration line. T
nput of nume
utput is cred
s variable in
nt wave pro
of Case #1.
ident wave p
e was measu
ve profile i
paddle contro
harbor mod
waves prop
efore this pr
numerical m
le, which is
Then, the sim
erical model
dible.
n Case #1, an
file. The Fig
profile in Ca
ured by Lep
in the prese
olled by com
del. Since th
agated in th
rofile is take
model simply
exerted in t
mulated wav
l is approach
nd the other
gure 4.9 sho
se #1
pelletier (198
ent numeric
mputer, and
he experimen
he water ba
en as the wa
y loads the
the numeric
es are initiat
hing to the re
factors are t
ows the incid
80) in the ex
cal model a
surface elev
nts were co
asin with n
ave that initi
wave prof
cal system th
ted in the pr
eal situation
the same, inc
dent wave p
xperiment, a
as well. Th
vation was r
onducted un
negligible di
ially came fr
file above a
hrough the i
esent model
as much as
44
cluding wate
rofile used i
and is used a
he wave wa
recorded nea
nder idealize
ispersion an
rom the wav
and create a
internal wav
l. By doing s
possible, an
er
in
as
as
ar
ed
nd
ve
an
ve
so,
nd
Case
The i
the ba
Figur
The s
boun
there
minu
1_1:
incident wav
athymetry o
re 4.10 The
star marks t
dary of incid
are 90,000
utes, and the
ve profile is
f the first mo
spatially dis
he location
dent waves.
(400×500)
numerical so
applied into
odel. The leg
scretized bat
of probe ga
The resolut
cells in the
olution is sh
o the 4 mode
gend assigns
thymetry of m
auge, and the
tion is define
e above mo
hown in Figu
els in Case 1
s the depths
model 1 in C
e yellow lin
ed as 5 mm
del. One ru
ure 4.11.
1, and Figur
with various
Case #1.
ne denotes th
( Δx) by 5 m
un takes app
45
re 4.10 show
s colors.
he generatio
mm ( Δy), an
proximately
ws
on
nd
2
Figur
surfa
Comp
F
As Fi
curve
Figure 4.
re 4.11 is the
ce elevation
pare the pres
Figure 4.12
igure 4.12, t
e except som
11 The pres
e numerical
n with time in
sent numeric
Comparison
the present n
me minor par
sent numeric
solution at t
n the middle
cal solution a
n between th
numerical mo
rts, which is
cal solution a
the location
e of the dept
and the expe
he present nu
odel matche
due to the sl
at probe gau
of probe gau
th inside bac
eriment as fo
umerical sol
es with the re
light dissipat
uge for Case
uge, so this
ck wall (star
ollow.
lution and ex
ecorded surf
ation.
46
1_1.
simulates th
r in Fig 4.10
xperiment
face elevatio
he
0).
on
Case
The i
bathy
Figu
The s
boun
there
2 min
1_2:
incident wav
ymetry of the
ure 4.13 The
star marks t
dary of incid
are 90,000
nutes, and Fi
ve profile is
e second mo
e spatially di
he location
dent waves.
(400×500) c
igure 4.14 sh
applied into
odel. The leg
scretized bat
of probe ga
The resolut
cells in the a
hows the num
o the 4 mode
gend assigns
thymetry of
auge, and the
tion is define
above model
merical solu
els in Case 1
the depths w
f model 2 in C
e yellow lin
ed as 5 mm
l. One run w
ution.
1, and Fig 4.
with various
Case #1.
ne denotes th
( Δx) by 5 m
would take a
47
.13 shows th
colors.
he generatio
mm ( Δy), an
approximatel
he
on
nd
ly
Figur
surfa
Comp
F
As F
eleva
Figure 4.
re 4.14 is the
ce elevation
pare the pres
Figure 4.15
igure 4.15,
ation curve.
14 The pres
e numerical
n with time in
sent numeric
Comparison
the present
sent numeric
solution at t
n the middle
cal solution a
n between th
numerical m
cal solution a
the location
e of the dept
and the expe
he present nu
model fairly
at probe gau
of probe gau
th inside bac
eriment as fo
umerical sol
y matches w
uge for Case
uge, so this
ck wall (star
ollow.
lution and ex
with the reco
48
1_2.
simulates th
r in Fig 4.13
xperiment
orded surfac
he
).
ce
Case
The i
bathy
Figu
The s
boun
there
2 min
1_3:
incident wav
ymetry of the
ure 4.16 The
star marks t
dary of incid
are 90,000
nutes, the nu
ve profile is
e third mode
e spatially di
he location
dent waves.
(400×500) c
umerical solu
applied into
el. The legen
scretized bat
of probe ga
The resolut
cells in the a
ution is show
o the 4 mode
nd assigns th
thymetry of
auge, and the
tion is define
above model
wn as Figure
els in Case 1
he depths wit
f model 3 in C
e yellow lin
ed as 5 mm
l. One run w
4.17.
1, and Fig 4.
th various co
Case #1.
ne denotes th
( Δx) by 5 m
would take a
49
.16 shows th
olors.
he generatio
mm ( Δy), an
approximatel
he
on
nd
ly
Figur
surfa
Comp
F
As F
eleva
Figure 4.
re 4.17 is the
ce elevation
pare the pres
Figure 4.18
igure 4.18,
ation curve.
17 The pres
e numerical
n with time in
sent numeric
Comparison
the present
sent numeric
solution at t
n the middle
cal solution a
n between th
numerical m
cal solution a
the location
e of the dept
and the expe
he present nu
model fairly
at probe gau
of probe gau
th inside bac
eriment as fo
umerical sol
y matches w
uge for Case
uge, so this
ck wall (star
ollow.
lution and ex
with the reco
50
1_3.
simulates th
r in Fig 4.16
xperiment
orded surfac
he
6).
ce
Case
The i
bathy
Figu
The s
boun
there
2 min
1_4:
incident wav
ymetry of the
ure 4.19 The
star marks t
dary of incid
are 90,000
nutes, Figure
ve profile is
e fourth mod
e spatially di
he location
dent waves.
(400×500) c
e 4.20 shows
applied into
del. The lege
scretized bat
of probe ga
The resolut
cells in the a
s the numeri
o the 4 mode
end assigns t
thymetry of
auge, and the
tion is define
above model
cal solution.
els in Case 1
the depths w
f model 4 in C
e yellow lin
ed as 5 mm
l. One run w
.
1, and Fig 4.
with various c
Case #1.
ne denotes th
( Δx) by 5 m
would take a
51
.19 shows th
colors.
he generatio
mm ( Δy), an
approximatel
he
on
nd
ly
Figur
surfa
Comp
F
As F
eleva
Figure 4.
re 4.20 is the
ce elevation
pare the pres
Figure 4.21
igure 4.21,
ation curve.
20 The pres
e numerical
n with time in
sent numeric
Comparison
the present
sent numeric
solution at t
n the middle
cal solution a
n between th
numerical m
cal solution a
the location
e of the dept
and the expe
he present nu
model fairly
at probe gau
of probe gau
th inside bac
eriment as fo
umerical sol
y matches w
uge for Case
uge, so this
ck wall (star
ollow.
lution and ex
with the reco
52
1_4.
simulates th
in Fig 4.19)
xperiment
orded surfac
he
)..
ce
4
Case
Table
botto
indic
The T
Table
M
4.3.2 Case #
#2 has rect
e 4.3, the in
m is unifor
ates gauge p
Table.4.5 exh
e 4.5 Dimen
Model
In
W
1 Fig
2 Fig
3 Fig
4 Fig
#2
tangular har
ncident wave
rmly flat. T
probe.
Figure 4.
hibits the sp
nsions of the
ncident
Wave
a
g. 4.23
g. 4.23
g. 4.23
g. 4.23
rbor model w
e is periodic
he harbor m
22 A typica
ecific dimen
e harbor mod
a (cm)
7.6
7.6
7.6
7.6
with ratio o
cal, the entra
model is ske
al plan view
nsions of the
dels in Case #
b (cm)
7.6
6.08
3.04
1.52
of length to
ance is parti
etched in F
of the harbo
e harbor mod
#2
l (cm)
38
38
38
38
width 5:1.
ially open, a
Figure 4.22,
or in case 2
dels in Case
h (cm)
10
10
10
10
53
As shown i
and the wate
and the sta
#2.
T (s)
2.0
2.0
2.0
2.0
in
er
ar
The o
same
incid
Fig
These
be us
was g
near t
condi
dissip
wave
create
intern
mode
much
opening wid
, including h
ent wave pro
gure 4.23 Inc
e wave prof
sed as the in
generated by
the entrance
itions, the w
pation. Ther
e generator.
e an inciden
nal wave gen
el. By doing
h as possible
dth of harbor
harbor size, w
ofile used in
cident wave
files were m
ncident wave
y a paddle c
e of harbor m
waves prop
efore this pr
The numeri
nt wave file,
neration line
so, the inpu
e, and the out
r entrance is
water depth
n all the 4 mo
profile in C
measured by L
e profiles in
controlled by
model. Since
agated in th
rofile could b
ical model w
which woul
e. Then, the s
ut of numeri
tput should b
variable in C
and incident
odels of Case
ase #2
Lepelletier (
the present
y computer,
the experim
he water ba
be taken as t
would simp
d be exerted
simulated wa
ical model is
be credible.
Case #2, and
nt wave profi
e #2.
(1980) in th
numerical m
, and surface
ments were c
asin with n
the wave tha
ply load the
d in the num
aves would
s approachin
d the other f
ile. Figure 4
he experimen
models as we
e elevation w
conducted un
negligible di
at initially c
wave profi
merical system
be initiated
ng to the rea
54
factors are th
.23 shows th
nt, and woul
ell. The wav
was recorde
nder idealize
ispersion an
ame from th
le above an
m through th
in the presen
al situation a
he
he
ld
ve
ed
ed
nd
he
nd
he
nt
as
Case
The i
bathy
Figur
The s
boun
there
minu
2_1 (100%
incident wav
ymetry of the
re 4.24 The
star marks t
dary of incid
are 90,000
utes, Figure 4
Open):
ve profile is
e first experi
spatially dis
he location
dent waves.
(400×500)
4.15 shows th
s applied int
iment. The l
scretized bat
of probe ga
The resolut
cells in the
he numerica
to 4 models
egend assign
thymetry of m
auge, and the
tion is define
e above mo
al solution.
s in Case 2,
ns the depths
model 1 in C
e yellow lin
ed as 5 mm
del. One ru
and Fig 4.2
s with variou
Case #2.
ne denotes th
( Δx) by 5 m
un takes app
55
24 shows th
us colors.
he generatio
mm ( Δy), an
proximately
he
on
nd
2
Figur
surfa
Comp
F
As F
eleva
Figure 4.
re 4.25 is the
ce elevation
pare the pres
Figure 4.26
igure 4.26,
ation curve.
25 The pres
e numerical
n with time in
sent numeric
Comparison
the present
sent numeric
solution at t
n the middle
cal solution a
n between th
numerical m
cal solution a
the location
e of the dept
and the expe
he present nu
model fairly
at probe gau
of probe gau
th inside bac
eriment as fo
umerical sol
y matches w
uge for Case
uge, so this
ck wall (star
ollow.
lution and ex
with the reco
56
2_1.
simulates th
in Fig 4.24)
xperiment
orded surfac
he
)..
ce
Case
The i
bathy
Figur
The s
boun
there
minu
2_2 (80% O
incident wav
ymetry of the
re 4.27 The
star marks t
dary of incid
are 90,000
utes, Figure 4
Open):
ve profile is
e second exp
spatially dis
he location
dent waves.
(400×500)
4.28 shows th
s applied int
periment. Th
scretized bat
of probe ga
The resolut
cells in the
he numerica
to 4 models
he legend ass
thymetry of m
auge, and the
tion is define
e above mo
al solution.
s in Case 2,
signs the dep
model 2 in C
e yellow lin
ed as 5 mm
del. One ru
and Fig 4.2
pths with var
Case #2.
ne denotes th
( Δx) by 5 m
un takes app
57
27 shows th
rious colors.
he generatio
mm ( Δy), an
proximately
he
.
on
nd
2
Figur
surfa
Comp
F
As F
eleva
Figure 4.
re 4.28 is the
ce elevation
pare the pres
Figure 4.29
igure 4.29,
ation curve.
28 The pres
e numerical
n with time in
sent numeric
Comparison
the present
sent numeric
solution at t
n the middle
cal solution a
n between th
numerical m
cal solution a
the location
e of the dept
and the expe
he present nu
model fairly
at probe gau
of probe gau
th inside bac
eriment as fo
umerical sol
y matches w
uge for Case
uge, so this
ck wall (star
ollow.
lution and ex
with the reco
58
2_2.
simulates th
r in Fig 4.27
xperiment
orded surfac
he
7).
ce
Case
The i
bathy
Figur
The s
boun
there
minu
2_3 (40% O
incident wav
ymetry of the
re 4.30 The
star marks t
dary of incid
are 90,000
utes, Figure 4
Open):
ve profile is
e third exper
spatially dis
he location
dent waves.
(400×500)
4.31 shows th
s applied int
riment. The l
scretized bat
of probe ga
The resolut
cells in the
he numerica
to 4 models
legend assig
thymetry of m
auge, and the
tion is define
e above mo
al solution.
s in Case 2,
gns the depth
model 3 in C
e yellow lin
ed as 5 mm
del. One ru
and Fig 4.3
hs with vario
Case #2.
ne denotes th
( Δx) by 5 m
un takes app
59
30 shows th
ous colors.
he generatio
mm ( Δy), an
proximately
he
on
nd
2
Figur
surfa
Comp
F
As F
eleva
Figure 4.
re 4.31 is the
ce elevation
pare the pres
Figure 4.32
igure 4.32,
ation curve.
31 The pres
e numerical
n with time in
sent numeric
Comparison
the present
sent numeric
solution at t
n the middle
cal solution a
n between th
numerical m
cal solution a
the location
e of the dept
and the expe
he present nu
model fairly
at probe gau
of probe gau
th inside bac
eriment as fo
umerical sol
y matches w
uge for Case
uge, so this
ck wall (star
ollow.
lution and ex
with the reco
60
2_3.
simulates th
r in Fig 4.30
xperiment
orded surfac
he
0).
ce
Case
The i
bathy
Figur
The s
boun
there
minu
2_4 (20% O
incident wav
ymetry of the
re 4.33 The
star marks t
dary of incid
are 90,000
utes, and Figu
Open):
ve profile is
e fourth expe
spatially dis
he location
dent waves.
(400×500)
ure 4.34 sho
s applied int
eriment. The
scretized bat
of probe ga
The resolut
cells in the
ws the nume
to 4 models
e legend assi
thymetry of m
auge, and the
tion is define
e above mo
erical solutio
s in Case 2,
igns the dept
model 4 in C
e yellow lin
ed as 5 mm
del. One ru
on.
and Fig 4.3
ths with vari
Case #2.
ne denotes th
( Δx) by 5 m
un takes app
61
30 shows th
ious colors.
he generatio
mm ( Δy), an
proximately
he
on
nd
2
Figur
surfa
Comp
F
As F
eleva
Figure 4.
re 4.34 is the
ce elevation
pare the pres
Figure 4.35
igure 4.35,
ation curve.
34 The pres
e numerical
n with time in
sent numeric
Comparison
the present
sent numeric
solution at t
n the middle
cal solution a
n between th
numerical m
cal solution a
the location
e of the dept
and the expe
he present nu
model fairly
at probe gau
of probe gau
th inside bac
eriment as fo
umerical sol
y matches w
uge for Case
uge, so this
ck wall (star
ollow.
lution and ex
with the reco
62
2_4.
simulates th
r in Fig 4.33
xperiment
orded surfac
he
).
ce
4
Case
Table
unifo
gauge
The T
Table
Sce
4.3.3 Case #
#3 has rect
e 4.3, the inc
ormly flat. T
e.
Table.4.6 exh
e 4.6 Dimen
enario
In
W
1 Fig
2 Fig
3 Fig
#3
tangular har
cident wave
he harbor m
Figure 4.
hibits the sp
nsions of the
ncident
Wave
a
g. 4.38
g. 4.41
g. 4.44
rbor model w
is transient
model is sket
36 A typica
ecific dimen
e harbor mod
a (cm)
7
7
7
with ratio o
t, the entranc
tched in Figu
al plan view
nsions of the
dels in Case #
l (cm)
35
35
35
of length to
ce is fully o
ure 4.36, and
of the harbo
e harbor mod
#3
h (cm)
8
8
8
width 5:1.
open, and wa
d the star in
or in case 3
dels in Case
63
As shown i
ater bottom
ndicates prob
#3.
in
is
be
The i
inclu
in all
Fig
The r
star m
boun
there
incident wav
ding water d
the 3 scenar
gure 4.37 Th
red color ind
marks the l
dary of incid
are 90,000 c
ve profile is
depth and ha
rios of Case
he spatially d
dicates the l
location of
dent waves.
cells in the a
variable in
arbor size. Th
#3.
discretized b
land area, an
probe gaug
The resolut
above model
Case #3, an
he Figure 4.3
bathymetry o
nd the blue
ge, and the
tion is define
l. One run w
nd the other
37 shows th
of the only ha
color repres
yellow line
ed as 5 mm
would take ap
factors rem
e only harbo
arbor model
sents the wa
e denotes th
( Δx) by 5 m
pprox.2 minu
64
main the same
or model use
l in Case #3
ater part. Th
he generatio
mm ( Δy), an
utes.
e,
ed
he
on
nd
Case
Fig
This
the i
gener
the e
condi
dissip
gener
incid
as we
the in
mode
much
3_1:
gure 4.38 Inc
wave profil
incident wav
rated by a p
entrance of h
itions, the w
pation. Ther
rator. The n
ent wave fil
ell as the sur
nternal wave
el. By doing
h as possible
cident wave
e was measu
ve profile i
paddle contro
harbor mod
waves prop
efore this pr
numerical m
le, which co
rface elevati
e generation
so, the inpu
e, and the out
profile of sc
ured by Lep
in the prese
olled by com
del. Since th
agated in th
rofile is take
model simply
ntains data o
on. These it
n line, and t
ut of numeri
tput should b
cenario 1 in
pelletier (198
ent numeric
mputer, and
he experimen
he water ba
en as the wa
y loads the
of volume fl
tems are exe
the simulate
ical model is
be credible.
Case #3
80) in the ex
cal model a
surface elev
nts were co
asin with n
ave that initi
wave profi
flux, surface
erted in the n
ed waves are
s approachin
xperiment, a
as well. Th
vation was r
onducted un
negligible di
ially came fr
ile above an
slope, surfa
numerical sy
e initiated i
ng to the rea
65
and is used a
he wave wa
recorded nea
nder idealize
ispersion an
rom the wav
nd creates a
ace curvature
ystem throug
n the presen
al situation a
as
as
ar
ed
nd
ve
an
e,
gh
nt
as
Figur
surfa
Comp
F
As F
eleva
Figure 4.3
re 4.39 is the
ce elevation
pare the pres
Figure 4.40
igure 4.40,
ation curve.
39 The pres
e numerical
n with time in
sent numeric
Comparison
the present
ent numeric
solution at t
n the middle
cal solution a
n between th
numerical m
al solution a
the location
e of the dept
and the expe
he present nu
model fairly
at probe gaug
of probe gau
th inside bac
eriment as fo
umerical sol
y matches w
ge for Case 3
uge, so this
ck wall (star
ollow.
lution and ex
with the reco
66
3_1.
simulates th
r in Fig 4.37
xperiment
orded surfac
he
7).
ce
Case
Fig
This
the i
gener
the e
condi
dissip
gener
incid
as we
the in
mode
much
3_2:
gure 4.41 Inc
wave profil
incident wav
rated by a p
entrance of h
itions, the w
pation. Ther
rator. The n
ent wave fil
ell as the sur
nternal wave
el. By doing
h as possible
cident wave
e was measu
ve profile i
paddle contro
harbor mod
waves prop
efore this pr
numerical m
le, which co
rface elevati
e generation
so, the inpu
e, and the out
profile of sc
ured by Lep
in the prese
olled by com
del. Since th
agated in th
rofile is take
model simply
ntains data o
on. These it
n line, and t
ut of numeri
tput should b
cenario 2 in
pelletier (198
ent numeric
mputer, and
he experimen
he water ba
en as the wa
y loads the
of volume fl
tems are exe
the simulate
ical model is
be credible.
Case #3
80) in the ex
cal model a
surface elev
nts were co
asin with n
ave that initi
wave profi
flux, surface
erted in the n
ed waves are
s approachin
xperiment, a
as well. Th
vation was r
onducted un
negligible di
ially came fr
ile above an
slope, surfa
numerical sy
e initiated i
ng to the rea
67
and is used a
he wave wa
recorded nea
nder idealize
ispersion an
rom the wav
nd creates a
ace curvature
ystem throug
n the presen
al situation a
as
as
ar
ed
nd
ve
an
e,
gh
nt
as
Figur
surfa
Comp
F
As F
eleva
Figure 4.4
re 4.42 is the
ce elevation
pare the pres
Figure 4.43
igure 4.43,
ation curve.
42 The pres
e numerical
n with time in
sent numeric
Comparison
the present
ent numeric
solution at t
n the middle
cal solution a
n between th
numerical m
al solution a
the location
e of the dept
and the expe
he present nu
model fairly
at probe gaug
of probe gau
th inside bac
eriment as fo
umerical sol
y matches w
ge for Case 3
uge, so this
ck wall (star
ollow.
lution and ex
with the reco
68
3_2.
simulates th
r in Fig 4.37
xperiment
orded surfac
he
7).
ce
Case
Fig
This
the i
gener
the e
condi
dissip
gener
incid
as we
the in
mode
much
3_3:
gure 4.44 Inc
wave profil
incident wav
rated by a p
entrance of h
itions, the w
pation. Ther
rator. The n
ent wave fil
ell as the sur
nternal wave
el. By doing
h as possible
cident wave
e was measu
ve profile i
paddle contro
harbor mod
waves prop
efore this pr
numerical m
le, which co
rface elevati
e generation
so, the inpu
e, and the out
profile of sc
ured by Lep
in the prese
olled by com
del. Since th
agated in th
rofile is take
model simply
ntains data o
on. These it
n line, and t
ut of numeri
tput should b
cenario 3 in
pelletier (198
ent numeric
mputer, and
he experimen
he water ba
en as the wa
y loads the
of volume fl
tems are exe
the simulate
ical model is
be credible.
Case #3
80) in the ex
cal model a
surface elev
nts were co
asin with n
ave that initi
wave profi
flux, surface
erted in the n
ed waves are
s approachin
xperiment, a
as well. Th
vation was r
onducted un
negligible di
ially came fr
ile above an
slope, surfa
numerical sy
e initiated i
ng to the rea
69
and is used a
he wave wa
recorded nea
nder idealize
ispersion an
rom the wav
nd creates a
ace curvature
ystem throug
n the presen
al situation a
as
as
ar
ed
nd
ve
an
e,
gh
nt
as
Figur
surfa
Comp
F
As F
eleva
Figure 4.4
re 4.45 is the
ce elevation
pare the pres
Figure 4.46
igure 4.46,
ation curve.
45 The pres
e numerical
n with time in
sent numeric
Comparison
the present
ent numeric
solution at t
n the middle
cal solution a
n between th
numerical m
al solution a
the location
e of the dept
and the expe
he present nu
model fairly
at probe gaug
of probe gau
th inside bac
eriment as fo
umerical sol
y matches w
ge for Case 3
uge, so this
ck wall (star
ollow.
lution and ex
with the reco
70
3_3.
simulates th
r in Fig 4.37
xperiment
orded surfac
he
7).
ce
4
Case
Table
botto
indic
The T
Table
Sce
4.3.4 Case #
#4 has rect
e 4.3, the in
m linearly
ates probe g
Figure
Table.4.7 exh
e 4.7 Dimen
enario
In
W
1 Fig
2 Fig
3 Fig
(
(b
#4
tangular har
ncident wave
rises up. Th
gauge.
e 4.47 (a). A
(b). A
hibits the sp
nsions of the
ncident
Wave
a
g. 4.49
g. 4.52
g. 4.55
a)
b)
rbor model w
e is transien
he harbor m
A typical pla
A typical side
ecific dimen
e harbor mod
a (cm)
20
20
20
with ratio o
nt, the entran
model is ske
an view of th
e view of the
nsions of the
dels in Case #
l (cm)
100
100
100
of length to
nce would b
etched in F
he harbor in c
e harbor in c
e harbor mod
#4
h (cm)
8
8
8
width 5:1.
be fully ope
Figure 4.47,
case 4.
case 4
dels in Case
ht (cm)
4
4
4
71
As shown i
en, and wate
and the sta
#4.
in
er
ar
The i
inclu
in all
Fig
The r
star m
boun
there
incident wav
ding water d
the 3 scenar
gure 4.48 Th
red color ind
marks the l
dary of incid
are 90,000 (
ve profile is
depth and ha
rios of Case
he spatially d
dicates the l
location of
dent waves.
(400×500) c
variable in
arbor size. Th
#4.
discretized b
land area, an
probe gaug
The resolut
cells in the ab
Case #4, an
he Figure 4.4
bathymetry o
nd the blue
ge, and the
tion is define
bove model.
nd the other
48 shows th
of the only ha
color repres
yellow line
ed as 5 mm
. One run tak
factors rem
e only harbo
arbor model
sents the wa
e denotes th
( Δx) by 5 m
kes approx. 2
72
main the same
or model use
l in Case #4
ater part. Th
he generatio
mm ( Δy), an
2 minutes.
e,
ed
he
on
nd
Case
Fig
This
the i
gener
the e
condi
dissip
gener
incid
as we
the in
mode
much
4_1:
gure 4.49 Inc
wave profil
incident wav
rated by a p
entrance of h
itions, the w
pation. Ther
rator. The n
ent wave fil
ell as the sur
nternal wave
el. By doing
h as possible
cident wave
e was measu
ve profile i
paddle contro
harbor mod
waves prop
efore this pr
numerical m
le, which co
rface elevati
e generation
so, the inpu
e, and the out
profile of sc
ured by Lep
in the prese
olled by com
del. Since th
agated in th
rofile is take
model simply
ntains data o
on. These it
n line, and t
ut of numeri
tput should b
cenario 1 in
pelletier (198
ent numeric
mputer, and
he experimen
he water ba
en as the wa
y loads the
of volume fl
tems are exe
the simulate
ical model is
be credible.
Case #4
80) in the ex
cal model a
surface elev
nts were co
asin with n
ave that initi
wave profi
flux, surface
erted in the n
ed waves are
s approachin
xperiment, a
as well. Th
vation was r
onducted un
negligible di
ially came fr
ile above an
slope, surfa
numerical sy
e initiated i
ng to the rea
73
and is used a
he wave wa
recorded nea
nder idealize
ispersion an
rom the wav
nd creates a
ace curvature
ystem throug
n the presen
al situation a
as
as
ar
ed
nd
ve
an
e,
gh
nt
as
Figur
surfa
Comp
F
As F
eleva
Figure 4.5
re 4.50 is the
ce elevation
pare the pres
Figure 4.51
igure 4.51,
ation curve.
50 The pres
e numerical
n with time in
sent numeric
Comparison
the present
ent numeric
solution at t
n the middle
cal solution a
n between th
numerical m
al solution a
the location
e of the dept
and the expe
he present nu
model fairly
at probe gaug
of probe gau
th inside bac
eriment as fo
umerical sol
y matches w
ge for Case 4
uge, so this
ck wall (star
ollow.
lution and ex
with the reco
74
4_1.
simulates th
r in Fig 4.48
xperiment
orded surfac
he
8).
ce
Case
Fig
This
the i
gener
the e
condi
dissip
gener
incid
as we
the in
mode
much
4_2:
gure 4.52 Inc
wave profil
incident wav
rated by a p
entrance of h
itions, the w
pation. Ther
rator. The n
ent wave fil
ell as the sur
nternal wave
el. By doing
h as possible
cident wave
e was measu
ve profile i
paddle contro
harbor mod
waves prop
efore this pr
numerical m
le, which co
rface elevati
e generation
so, the inpu
e, and the out
profile of sc
ured by Lep
in the prese
olled by com
del. Since th
agated in th
rofile is take
model simply
ntains data o
on. These it
n line, and t
ut of numeri
tput should b
cenario 2 in
pelletier (198
ent numeric
mputer, and
he experimen
he water ba
en as the wa
y loads the
of volume fl
tems are exe
the simulate
ical model is
be credible.
Case #4
80) in the ex
cal model a
surface elev
nts were co
asin with n
ave that initi
wave profi
flux, surface
erted in the n
ed waves are
s approachin
xperiment, a
as well. Th
vation was r
onducted un
negligible di
ially came fr
ile above an
slope, surfa
numerical sy
e initiated i
ng to the rea
75
and is used a
he wave wa
recorded nea
nder idealize
ispersion an
rom the wav
nd creates a
ace curvature
ystem throug
n the presen
al situation a
as
as
ar
ed
nd
ve
an
e,
gh
nt
as
Figur
surfa
Comp
F
As F
eleva
Figure 4.5
re 4.53 is the
ce elevation
pare the pres
Figure 4.54
igure 4.54,
ation curve.
53 The pres
e numerical
n with time in
sent numeric
Comparison
the present
ent numeric
solution at t
n the middle
cal solution a
n between th
numerical m
al solution a
the location
e of the dept
and the expe
he present nu
model fairly
at probe gaug
of probe gau
th inside bac
eriment as fo
umerical sol
y matches w
ge for Case 4
uge, so this
ck wall (star
ollow.
lution and ex
with the reco
76
4_2.
simulates th
r in Fig 4.48
xperiment
orded surfac
he
8).
ce
Case
Fig
This
the i
gener
the e
condi
dissip
gener
incid
as we
the in
mode
much
4_3:
gure 4.55 Inc
wave profil
incident wav
rated by a p
entrance of h
itions, the w
pation. Ther
rator. The n
ent wave fil
ell as the sur
nternal wave
el. By doing
h as possible
cident wave
e was measu
ve profile i
paddle contro
harbor mod
waves prop
efore this pr
numerical m
le, which co
rface elevati
e generation
so, the inpu
e, and the out
profile of sc
ured by Lep
in the prese
olled by com
del. Since th
agated in th
rofile is take
model simply
ntains data o
on. These it
n line, and t
ut of numeri
tput should b
cenario 3 in
pelletier (198
ent numeric
mputer, and
he experimen
he water ba
en as the wa
y loads the
of volume fl
tems are exe
the simulate
ical model is
be credible.
Case #4
80) in the ex
cal model a
surface elev
nts were co
asin with n
ave that initi
wave profi
flux, surface
erted in the n
ed waves are
s approachin
xperiment, a
as well. Th
vation was r
onducted un
negligible di
ially came fr
ile above an
slope, surfa
numerical sy
e initiated i
ng to the rea
77
and is used a
he wave wa
recorded nea
nder idealize
ispersion an
rom the wav
nd creates a
ace curvature
ystem throug
n the presen
al situation a
as
as
ar
ed
nd
ve
an
e,
gh
nt
as
Figur
surfa
Comp
F
As F
eleva
Figure 4.5
re 4.56 is the
ce elevation
pare the pres
Figure 4.57
igure 4.57,
ation curve.
56 The pres
e numerical
n with time in
sent numeric
Comparison
the present
ent numeric
solution at t
n the middle
cal solution a
n between th
numerical m
al solution a
the location
e of the dept
and the expe
he present nu
model fairly
at probe gaug
of probe gau
th inside bac
eriment as fo
umerical sol
y matches w
ge for Case 4
uge, so this
ck wall (star
ollow.
lution and ex
with the reco
78
4_3.
simulates th
r in Fig 4.48
xperiment
orded surfac
he
8).
ce
79
4.4 Group B: Trapezoidal Harbor
Group B has 2 cases all together, and their common place is that the harbor models are
trapezoidal. For all the rectangular harbors, the entrance width to end wall width is 5:1,
and the entrance width to the length is 0.16. The gauge probe is installed in the middle of
the back wall at deep end of the harbor models. There are two variable factors, including
incident wave amplitude, and entrance blockage. The incident waves are damping
transient waves for both Case 5 and Case 6; The entrance blockage is quantified with the
percentage of opening width; Water bottom profile is constantly flat for all the models in
Group B. These variable factors are organized with different combinations, and setup of
Case 5 and Case 6 are specifically described in Table 4.8.
Table 4.8 The characters of harbor models in Group B
Content Case 5 Case 6
Incident Wave transient transient
Wave
Amplitude
multiple single
Entrance 100% open ≤ 100% open
Water Bottom constant constant
In Case #5, different wave amplitude is used in each scenario, whereas Case #6 has
variable entrance opening width for each model.
4
Case
and t
transi
sketc
The T
Table
Sce
4.4.1 Case #
#5 has trape
the entrance
ient, the ent
hed in Figur
Figure
Table.4.9 exh
e 4.9 Dimen
enario
In
W
1 Fig
2 Fig
3 Fig
#5
ezoidal harb
width to th
trance is full
re 4.58, and
e 4.58 A typ
hibits the sp
nsions of the
ncident
Wave
a
g. 4.60
g. 4.63
g. 4.66
bor model wi
e length 0.1
ly open, and
the star indic
pical plan vi
ecific dimen
e harbor mod
a (cm)
19.5
19.5
19.5
ith ratio of e
6 . As show
d water botto
cates probe g
ew of the ha
nsions of the
dels in Case #
at (cm)
3.9
3,9
3,9
entrance wid
wn in Table
om is const
gauge.
arbor in case
e harbor mod
#5
l (cm)
122
122
122
dth to end w
4.8, the inci
ant. The har
e 5.
dels in Case
h (cm)
8
8
8
80
wall width 5:
ident wave
rbor model
#5.
1,
is
is
The i
inclu
in all
Fig
The r
star m
boun
there
incident wav
ding water d
the 3 scenar
gure 4.59 Th
red color ind
marks the l
dary of incid
are 90,000 (
ve profile is
depth and ha
rios of Case
he spatially d
dicates the l
location of
dent waves.
(400×500) c
variable in
arbor size. Th
#5.
discretized b
land area, an
probe gaug
The resolut
cells in the ab
Case #5, an
he Figure 4.5
bathymetry o
nd the blue
ge, and the
tion is define
bove model.
nd the other
59 shows th
of the only ha
color repres
yellow line
ed as 5 mm
. One run tak
factors rem
e only harbo
arbor model
sents the wa
e denotes th
( Δx) by 5 m
kes approx. 2
81
main the same
or model use
l in Case #5
ater part. Th
he generatio
mm ( Δy), an
2 minutes.
e,
ed
he
on
nd
Case
Fig
This
the i
gener
the e
condi
dissip
gener
incid
as we
the in
mode
much
5_1:
gure 4.60 Inc
wave profil
incident wav
rated by a p
entrance of h
itions, the w
pation. Ther
rator. The n
ent wave fil
ell as the sur
nternal wave
el. By doing
h as possible
cident wave
e was measu
ve profile i
paddle contro
harbor mod
waves prop
efore this pr
numerical m
le, which co
rface elevati
e generation
so, the inpu
e, and the out
profile of sc
ured by Lep
in the prese
olled by com
del. Since th
agated in th
rofile is take
model simply
ntains data o
on. These it
n line, and t
ut of numeri
tput should b
cenario 1 in
pelletier (198
ent numeric
mputer, and
he experimen
he water ba
en as the wa
y loads the
of volume fl
tems are exe
the simulate
ical model is
be credible.
Case #5
80) in the ex
cal model a
surface elev
nts were co
asin with n
ave that initi
wave profi
flux, surface
erted in the n
ed waves are
s approachin
xperiment, a
as well. Th
vation was r
onducted un
negligible di
ially came fr
ile above an
slope, surfa
numerical sy
e initiated i
ng to the rea
82
and is used a
he wave wa
recorded nea
nder idealize
ispersion an
rom the wav
nd creates a
ace curvature
ystem throug
n the presen
al situation a
as
as
ar
ed
nd
ve
an
e,
gh
nt
as
Figur
surfa
Comp
F
As F
eleva
Figure 4.6
re 4.61 is the
ce elevation
pare the pres
Figure 4.62
igure 4.62,
ation curve.
61 The pres
e numerical
n with time in
sent numeric
Comparison
the present
ent numeric
solution at t
n the middle
cal solution a
n between th
numerical m
al solution a
the location
e of the dept
and the expe
he present nu
model fairly
at probe gaug
of probe gau
th inside bac
eriment as fo
umerical sol
y matches w
ge for Case 5
uge, so this
ck wall (star
ollow.
lution and ex
with the reco
83
5_1.
simulates th
r in Fig 4.59
xperiment
orded surfac
he
9).
ce
Case
Fig
This
the i
gener
the e
condi
dissip
gener
incid
as we
the in
mode
much
5_2:
gure 4.63 Inc
wave profil
incident wav
rated by a p
entrance of h
itions, the w
pation. Ther
rator. The n
ent wave fil
ell as the sur
nternal wave
el. By doing
h as possible
cident wave
e was measu
ve profile i
paddle contro
harbor mod
waves prop
efore this pr
numerical m
le, which co
rface elevati
e generation
so, the inpu
e, and the out
profile of sc
ured by Lep
in the prese
olled by com
del. Since th
agated in th
rofile is take
model simply
ntains data o
on. These it
n line, and t
ut of numeri
tput should b
cenario 2 in
pelletier (198
ent numeric
mputer, and
he experimen
he water ba
en as the wa
y loads the
of volume fl
tems are exe
the simulate
ical model is
be credible.
Case #5
80) in the ex
cal model a
surface elev
nts were co
asin with n
ave that initi
wave profi
flux, surface
erted in the n
ed waves are
s approachin
xperiment, a
as well. Th
vation was r
onducted un
negligible di
ially came fr
ile above an
slope, surfa
numerical sy
e initiated i
ng to the rea
84
and is used a
he wave wa
recorded nea
nder idealize
ispersion an
rom the wav
nd creates a
ace curvature
ystem throug
n the presen
al situation a
as
as
ar
ed
nd
ve
an
e,
gh
nt
as
Figur
surfa
Comp
F
As F
eleva
Figure 4.6
re 4.64 is the
ce elevation
pare the pres
Figure 4.65
igure 4.65,
ation curve.
64 The pres
e numerical
n with time in
sent numeric
Comparison
the present
ent numeric
solution at t
n the middle
cal solution a
n between th
numerical m
al solution a
the location
e of the dept
and the expe
he present nu
model fairly
at probe gaug
of probe gau
th inside bac
eriment as fo
umerical sol
y matches w
ge for Case 5
uge, so this
ck wall (star
ollow.
lution and ex
with the reco
85
5_2.
simulates th
r in Fig 4.59
xperiment
orded surfac
he
9).
ce
Case
Fig
This
the i
gener
the e
condi
dissip
gener
incid
as we
the in
mode
much
5_3:
gure 4.66 Inc
wave profil
incident wav
rated by a p
entrance of h
itions, the w
pation. Ther
rator. The n
ent wave fil
ell as the sur
nternal wave
el. By doing
h as possible
cident wave
e was measu
ve profile i
paddle contro
harbor mod
waves prop
efore this pr
numerical m
le, which co
rface elevati
e generation
so, the inpu
e, and the out
profile of sc
ured by Lep
in the prese
olled by com
del. Since th
agated in th
rofile is take
model simply
ntains data o
on. These it
n line, and t
ut of numeri
tput should b
cenario 3 in
pelletier (198
ent numeric
mputer, and
he experimen
he water ba
en as the wa
y loads the
of volume fl
tems are exe
the simulate
ical model is
be credible.
Case #5
80) in the ex
cal model a
surface elev
nts were co
asin with n
ave that initi
wave profi
flux, surface
erted in the n
ed waves are
s approachin
xperiment, a
as well. Th
vation was r
onducted un
negligible di
ially came fr
ile above an
slope, surfa
numerical sy
e initiated i
ng to the rea
86
and is used a
he wave wa
recorded nea
nder idealize
ispersion an
rom the wav
nd creates a
ace curvature
ystem throug
n the presen
al situation a
as
as
ar
ed
nd
ve
an
e,
gh
nt
as
Figur
surfa
Comp
F
As F
eleva
Figure 4.6
re 4.67 is the
ce elevation
pare the pres
Figure 4.68
igure 4.68,
ation curve.
67 The pres
e numerical
n with time in
sent numeric
Comparison
the present
ent numeric
solution at t
n the middle
cal solution a
n between th
numerical m
al solution a
the location
e of the dept
and the expe
he present nu
model fairly
at probe gaug
of probe gau
th inside bac
eriment as fo
umerical sol
y matches w
ge for Case 5
uge, so this
ck wall (star
ollow.
lution and ex
with the reco
87
5_3.
simulates th
r in Fig 4.59
xperiment
orded surfac
he
9).
ce
4
Case
and t
transi
sketc
The T
Table
M
4.4.2 Case #
#6 has trape
the entrance
ient, the ent
hed in Figur
Table.4.10 ex
e 4.10 Dime
Model
In
W
1 Fig
2 Fig
3 Fig
4 Fig
#6
ezoidal harb
width to th
trance is full
re 4.69, and
Figure 4.
xhibits the s
ensions of th
ncident
Wave
a
g. 4.70
g. 4.70
g. 4.70
g. 4.70
bor model wi
e length 0.1
ly open, and
the star indic
69 A typica
pecific dime
he harbor mo
a (cm)
19.5
19.5
19.5
19.5
ith ratio of e
6 . As show
d water botto
cates probe g
al plan view
ensions of th
odels in Case
b (cm)
9.8
4.9
2.5
1.2
entrance wid
wn in Table
om is const
gauge.
of the harbo
he harbor mo
e #6
at (cm)
3.9
3.9
3.9
3.9
dth to end w
4.8, the inci
ant. The har
or in case 6
odels in Case
l (cm)
122
122
122
122
88
wall width 5:
ident wave
rbor model
e #6.
h (cm)
8
8
8
8
1,
is
is
The o
same
incid
Fig
These
as th
gener
the e
condi
dissip
gener
incid
gener
the in
the ou
opening wid
, including h
ent wave pro
gure 4.70 Inc
e wave prof
e incident w
rated by a p
entrance of h
itions, the w
pation. There
rator. The n
ent wave fil
ration line. T
nput of nume
utput should
dth of harbor
harbor size, w
ofile used in
cident wave
files were me
wave profile
paddle contro
harbor mod
waves prop
efore this pr
numerical m
le, which is
Then, the sim
erical model
d be credible
r entrance is
water depth
n all the 4 mo
profile in C
easured by L
es in the pre
olled by com
del. Since th
agated in th
rofile is take
model simply
exerted in t
mulated wav
l is approach
e.
variable in C
and incident
odels of Case
ase #6
Lepelletier (
esent numer
mputer, and
he experimen
he water ba
n as the wav
y loads the
the numeric
es are initiat
hing to the re
Case #6, and
nt wave profi
e #6.
(1980) in the
rical models
surface elev
nts were co
asin with n
ve that initia
wave profi
cal system th
ted in the pr
eal situation
d the other f
ile. Figure 4
e experimen
s as well. Th
vation was r
onducted un
negligible di
ally comes fr
ile above an
hrough the i
esent model
as much as
89
factors are th
.70 shows th
nt, and is use
he wave wa
recorded nea
nder idealize
ispersion an
from the wav
nd creates a
internal wav
l. By doing s
possible, an
he
he
ed
as
ar
ed
nd
ve
an
ve
so,
nd
Case
The i
bathy
Figur
The s
boun
there
minu
6_1 (50% O
incident wav
ymetry of the
re 4.71 The
star marks t
dary of incid
are 90,000
utes.
Open):
ve profile is
e first experi
spatially dis
he location
dent waves.
(400×500)
s applied int
iment. The l
scretized bat
of probe ga
The resolut
cells in the
to 4 models
egend assign
thymetry of m
auge, and the
tion is define
e above mo
s in Case 6,
ns the depths
model 1 in C
e yellow lin
ed as 5 mm
del. One ru
and Fig 4.7
s with variou
Case #6.
ne denotes th
( Δx) by 5 m
un takes app
90
71 shows th
us colors.
he generatio
mm ( Δy), an
proximately
he
on
nd
2
Figur
surfa
Comp
F
As F
eleva
Figure 4.
re 4.72 is the
ce elevation
pare the pres
Figure 4.73
igure 4.73,
ation curve.
72 The pres
e numerical
n with time in
sent numeric
Comparison
the present
sent numeric
solution at t
n the middle
cal solution a
n between th
numerical m
cal solution a
the location
e of the dept
and the expe
he present nu
model fairly
at probe gau
of probe gau
th inside bac
eriment as fo
umerical sol
y matches w
uge for Case
uge, so this
ck wall (star
ollow.
lution and ex
with the reco
91
6_1.
simulates th
r in Fig 4.71
xperiment
orded surfac
he
).
ce
Case
The i
bathy
Figur
The s
boun
there
minu
6_2 (25% O
incident wav
ymetry of the
re 4.74 The
star marks t
dary of incid
are 90,000
utes.
Open):
ve profile is
e second exp
spatially dis
the location
dent waves.
(400×500)
s applied int
periment. Th
scretized bat
of probe ga
The resolut
cells in the
to 4 models
he legend ass
thymetry of m
age, and the
tion is define
e above mo
s in Case 6,
signs the dep
model 2 in C
e yellow lin
ed as 5 mm
del. One ru
and Fig 4.7
pths with var
Case #6.
ne denotes th
( Δx) by 5 m
un takes app
92
74 shows th
rious colors.
he generatio
mm ( Δy), an
proximately
he
.
on
nd
2
Figur
surfa
Comp
F
As F
eleva
Figure 4.
re 4.75 is the
ce elevation
pare the pres
Figure 4.76
igure 4.76,
ation curve.
75 The pres
e numerical
n with time in
sent numeric
Comparison
the present
sent numeric
solution at t
n the middle
cal solution a
n between th
numerical m
cal solution a
the location
e of the dept
and the expe
he present nu
model fairly
at probe gau
of probe gau
th inside bac
eriment as fo
umerical sol
y matches w
uge for Case
uge, so this
ck wall (star
ollow.
lution and ex
with the reco
93
6_2.
simulates th
r in Fig 4.74
xperiment
orded surfac
he
4).
ce
Case
The i
bathy
Figur
The s
boun
there
minu
6_3 (12.5%
incident wav
ymetry of the
re 4.77 The
star marks t
dary of incid
are 90,000
utes.
% Open):
ve profile is
e third exper
spatially dis
he location
dent waves.
(400×500)
s applied int
riment. The l
scretized bat
of probe ga
The resolut
cells in the
to 4 models
legend assig
thymetry of m
auge, and the
tion is define
e above mo
s in Case 6,
gns the depth
model 3 in C
e yellow lin
ed as 5 mm
del. One ru
and Fig 4.7
hs with vario
Case #6.
ne denotes th
( Δx) by 5 m
un takes app
94
77 shows th
ous colors.
he generatio
mm ( Δy), an
proximately
he
on
nd
2
Figur
surfa
Comp
F
As F
eleva
Figure 4.
re 4.78 is the
ce elevation
pare the pres
Figure 4.79
igure 4.79,
ation curve.
78 The pres
e numerical
n with time in
sent numeric
Comparison
the present
sent numeric
solution at t
n the middle
cal solution a
n between th
numerical m
cal solution a
the location
e of the dept
and the expe
he present nu
model fairly
at probe gau
of probe gau
th inside bac
eriment as fo
umerical sol
y matches w
uge for Case
uge, so this
ck wall (star
ollow.
lution and ex
with the reco
95
6_3.
simulates th
r in Fig 4.77
xperiment
orded surfac
he
7).
ce
Case
The i
bathy
Figur
The s
boun
there
minu
6_4 (6.25%
incident wav
ymetry of the
re 4.80 The
star marks t
dary of incid
are 90,000
utes.
% Open):
ve profile is
e fourth expe
spatially dis
the location
dent waves.
(400×500)
s applied int
eriment. The
scretized bat
of probe ga
The resolut
cells in the
to 4 models
e legend assi
thymetry of m
age, and the
tion is define
e above mo
s in Case 6,
igns the dept
model 4 in C
e yellow lin
ed as 5 mm
del. One ru
and Fig 4.8
ths with vari
Case #6.
ne denotes th
( Δx) by 5 m
un takes app
96
80 shows th
ious colors.
he generatio
mm ( Δy), an
proximately
he
on
nd
2
Figur
surfa
Comp
F
As F
eleva
Figure 4.
re 4.81 is the
ce elevation
pare the pres
Figure 4.82
igure 4.82,
ation curve.
81 The pres
e numerical
n with time in
sent numeric
Comparison
the present
sent numeric
solution at t
n the middle
cal solution a
n between th
numerical m
cal solution a
the location
e of the dept
and the expe
he present nu
model fairly
at probe gau
of probe gau
th inside bac
eriment as fo
umerical sol
y matches w
uge for Case
uge, so this
ck wall (star
ollow.
lution and ex
with the reco
97
6_4.
simulates th
r in Fig 4.80
xperiment
orded surfac
he
0).
ce
98
4.5 Summary
In this chapter, the present numerical model is validated through simulating some simple
harbor model and comparing with the experiment records.
At the beginning, the experiment setup and numerical model setup are introduced
specifically. The essential concept of the experiment is to generate several wave trains
inside water basin, and let them travel into the harbor models with different characters.
The relevant characters include harbor size, harbor shape, entrance width, and water
bottom profile, which covers fairly enough complexity in the harbor models under
laboratory circumstances. The surface elevation in the middle of back wall was recorded
by a gauge system, and then is used as the reference to validate the numerical model.
Exactly the same characters and dimensions are adopted to build the numerical model,
and the simulated surface elevation at the same location of the gauge system is extracted
as well. Then, this simulated surface elevation is compare with the observed surface
elevation.
With the same incident waves and boundary conditions, the numerical model is
reliable, if the discrepancy between the two curves are small. There are six cases in this
chapter and they are treated with the same procedure. The present numerical solution is
observed to match with the experimental record, and this proves the potential for further
study in the real harbors.
99
CHAPTER 5: HARBOR OSCILLATION ON MEAN TIDAL LEVEL
In the previous chapter, study is focused on laboratory conditions and is easy to observe.
Nevertheless, the ultimate purpose of the present study is to research oscillation in the
real harbors. This will involve with more complexity, such as the bathymetry of real
harbors, tidal level fluctuations, the layout/bathymetry changing due to the tidal level
fluctuation, and the unknown incident wave profile. Unlike the laboratory model, the
harbor in reality is constantly changing both in temporal range and in spatial extent. In
this situation, it is necessary to investigate each of the contributor of the uncertainty and
to determine their impact in the natural process of harbor oscillations.
As the beginning, Chapter 5 discusses harbor oscillation on mean tidal level (MTL).
By doing so, the conclusion of earlier research will be ascertained and complemented,
which will further validate the present numerical model. Besides, this chapter also briefly
introduces the background information of concerned harbors.
The boundary conditions are defined by the layout and orientation of the harbor,
which will be impossible without investigating the harbors specifically. The present study
uses various sources of data to guarantee reliable and accurate boundary conditions, such
as navigation chart from National Oceanic & Atmospheric Administration (NOAA),
Google maps, Google earth, Jeppesen navigational chart database, and online pictures (or
videos) posted by local individuals.
5.1 C
Cresc
name
vulne
Figur
the re
The
Cresc
Figur
(a).
(c).
Crescent Cit
cent City, a
ed for its cre
erable to tsun
re 5.1 descri
ed pin mark)
(b) illustrat
cent City har
re 5.1 (a) Cr
ty Harbor,
small town
scent shape
namis from t
ibes the loca
) in the Unit
es the outer
rbor, and the
rescent City
California
n located on
of beach on
the Pacific o
ation of Cre
ted States, a
r area and
e yellow star
on the West
n the northw
the south. C
ocean due to
escent City h
nd it’s near
nearby shor
r indicates th
t Coast; (b) &
(b).
western corn
Crescent City
its location
harbor. The
to the middl
reline. The
he location o
& (c) Zoom-
ner of Califo
y is well kno
and topogra
(a) shows th
le point of th
(c) is the
of tidal gauge
-in; (Google
10
ornia state,
own for bein
aphy.
he harbor (a
he west coas
bird view o
e station.
e maps)
0
is
ng
as
st.
of
5
For th
After
mark
the ge
Figur
The r
The t
is an
conse
hours
5.1.1 Model
he present s
r spatial disc
ks the genera
eneration bo
re 5.2 The la
resolution is
time step Δt
n arbitrary c
equent linear
s costs appro
l Setup
study, the ba
cretization, o
ation bounda
oundary of in
ayout and ba
defined as 9
is 0.4 s, Cou
constant in
r dispersion
ox. 90 minut
athymetry of
one digital m
ary of incom
ncoming wav
athymetry of
9 m ( Δx) by
urant numbe
Eq. 3.15~E
relation wit
tes of compu
l
f Crescent C
map file is ac
ming waves f
ves from we
f Crescent C
9 m ( Δy), an
r is 0.638, an
Eq. 3.17, an
th Stokes fir
uter work, an
City harbor i
cquired as Fi
from south,
est. Tidal stat
City on mean
nd there are
nd dispersio
nd is determ
st order theo
nd Table 4.1
is used in th
igure 5.2. Th
and the grey
ation is mark
n tidal level (
127,300 (33
on coefficien
mined by ca
ory. The sim
1 shows the
10
he simulation
he orange lin
y line denote
ked by star.
(MTL)
35×380) cell
nt B is 1/15. B
alibrating th
mulation of 2
configuratio
1
n.
ne
es
s.
B
he
24
on
of the
along
as we
The
distri
proce
vario
small
harbo
break
on th
natur
with
is abs
e computati
g the orange
est source.
Figure 5.3
above incid
ibuted spectr
ess, however
us frequency
l to prevent
or oscillation
king wave is
he south and
ral condition
different po
sorbed and th
onal power.
line in Figu
The inciden
dent wave is
rum in a giv
r we can use
y of long w
overtopping
n itself. Sin
negligible.
d west side,
n as much as
orosity, based
he incident w
Figure 5.3
ure 5.2 as so
nt wave for w
s an idealiz
ven frequenc
e this wave
waves. The am
g or inundatio
nce the wav
Sponge laye
, and the pa
s possible. D
d on its char
wave interac
illustrates th
outh source,
white noise a
zed profile,
cy range. It
train as a to
mplitude of
on. So that,
ves have lon
er is defined
artially refle
Different seg
racter and te
cts with coas
he incident
and along th
analysis in C
which is ge
is not what
ool to inspe
f incident wa
the simulati
ng period (
along the ex
ective coastl
gment along
exture. Ther
stline as in th
waves. The
he grey line
Crescent City
enerated fro
t happened i
ct harbor be
ave is set to
ion is concen
≥ 12 min),
xterior bound
line is set t
the coastlin
efore, the ra
he nature.
10
ey are applie
in Figure 5.
y harbor
om uniforml
in the natura
ehavior unde
be relativel
ntrated on th
the issue o
dary of ocea
to imitate th
ne is assigne
adiated wave
2
ed
.2
ly
al
er
ly
he
of
an
he
ed
es
5
Figu
Figu
The a
surfa
spect
and t
from
5.1.2 Result
ure 5.4 The p
ure 5.5 The p
above curves
ce elevation
tral density d
the same inc
west source
ts
predicted res
predicted res
s are the num
n along time
distribution
cident wave
e.
sponse at tid
sponse at tid
merical solut
at the star in
as in Fig 5.6
from south
dal station in
dal station in
tion at the lo
n Fig 5.2. T
6. The reson
h source ind
Crescent Ci
Crescent Ci
ocation of tid
Transform th
nant mode is
duces more i
ity harbor (s
ity harbor (w
dal gauge, so
e time doma
s at period o
intensive os
10
south source)
west source)
o they predic
ain result int
of 20 minute
cillation tha
3
)
ct
to
es
an
Figur
wave
when
To as
adopt
curve
the d
chara
harbo
facin
Figure
re 5.6 is the
e frequency.
n water depth
scertain this
ted mild-slo
e at tidal gau
dimensionles
acteristic wav
or. In this ca
g coastal lin
e 5.6 Spectra
e spectra of
It shows tha
h at the tidal
result, it is
pe equation
uge station a
ss variable k
velength of
ase, l is take
ne, as shown
a of oscillati
white-noise
at the resona
gauge statio
necessary t
to analyze
as in Figure
kl, where k
incoming w
en as the seg
n in Figure 5
2
22.8 mi
25.4 min
on in Cresce
e analysis, a
ant mode of
on is 2.3 m.
to review pr
Crescent Ci
5.7. In the r
=
ଶగ
is the
waves, and l s
gment betwe
.2. The y ax
20 min
18.2
1.8 min
in
ent City harb
and the varia
f Crescent C
revious work
ity harbor, a
response cur
wave numb
stands for th
een the outer
xis represent
2 min
16.5 min
15.2
bor
able in horiz
City harbor i
k. The Xing
and acquires
rve, the x ax
ber. The L r
he characteri
r harbor entr
ts the amplif
min
13.3 min
12.4 m
10
zontal axis
s 20 minute
g et al. (2012
the respons
xis represent
represents th
istic length o
rance and th
fication facto
min
4
is
s,
2)
se
ts
he
of
he
or
R, w
ampl
labor
curve
resea
Xing
minu
equat
which is defi
itude outsid
ratory model
e, the experi
arch funding
et al. (2012
utes. This res
tion (nonline
Figure 5
fined as rati
e the harbor
l can follow
iments in sm
. After the n
2) acquires th
sult is close
ear model).
5.7 Amplific
2
io of the w
r. The advan
the same cu
maller water
numerical an
he Figure 5.7
to the 20 m
cation factor
22 min
wave amplitu
ntage of dim
urves as the
r basin can
nalysis with
7, which sho
minutes from
r at tidal gau
10.3 m
ude at the t
mensionless r
real harbor
be designed
h mild-slope
ows that the
m present stu
uge with resp
min
7.9 min
tidal gauge
response cur
do. With th
d, which ca
equation (l
first resonan
udy with Bou
pect to kl
6.6 min
10
to the wav
rve is that th
he help of th
an save muc
inear model
nt mode is 2
ussinesq-typ
n
5
ve
he
is
ch
l),
22
pe
5.2 L
Los A
on th
in the
harbo
coast
LA/L
Figur
(a).
(c).
Los Angeles
Angeles port
he south coas
e United Sta
or (as the re
t. The (b) ill
LB port, and
re 5.8 (a) LA
s/Long Beac
t and long B
st of Los An
ates. Figure 5
ed pin mark)
ustrates the
the yellow s
A/LB port on
ch Port, Cal
Beach port ar
ngeles Count
5.8 describe
) in the Uni
outer area a
star indicates
n the West C
lifornia
re two neigh
ty, and they
es the locatio
ted States, a
and nearby s
s the location
Coast; (b) &
(b).
hboring harb
are the Top
on of LA/LB
and it’s at th
shoreline. Th
n of tidal ga
(c) Zoom-in
bors in the Sa
p 2 busiest co
B port. The
he south end
he (c) is the
auge.
n; (Google m
10
an Pedro Ba
ontainer port
(a) shows th
d of the we
e bird view o
maps)
6
ay
ts
he
st
of
5
For t
spatia
mark
the ge
Figur
The r
cells
is 0.6
3.15~
with
comp
5.2.1 Model
the present
al discretiza
ks the genera
eneration bo
re 5.9 The la
resolution is
in the above
684, and th
~Eq. 3.17, an
Stokes first
puter work, a
l Setup
study, the b
ation, one d
ation bounda
oundary of in
ayout and ba
s defined as
e model. In t
he dispersion
nd is determ
t order theo
and Table 4.
bathymetry o
igital map f
ary of incom
ncoming wav
athymetry of
20 m ( Δx) b
the present m
n coefficien
mined by cali
ory. The sim
1 shows the
of LA/LB p
file is acqui
ming waves f
ves from we
f LA/LB por
by 20 m ( Δy
model, the t
nt B is 1/15
ibrating the
mulation of 7
configuratio
port is used
ired as Figu
from south,
est. Tidal stat
rt on mean ti
y), and ther
time step Δt
5. B is an a
consequent
72 hours co
on of the com
in the simu
ure 5.9. The
and the grey
ation is mark
idal level (M
re are 382,50
is 0.8 s, Co
arbitrary con
linear dispe
osts approx.
mputational
10
ulation. Afte
e orange lin
y line denote
ked by star.
MTL)
00 (750×510
urant numbe
nstant in Eq
ersion relatio
12 hours o
power.
7
er
ne
es
0)
er
q.
on
of
Figur
Figur
Figur
The
distri
proce
vario
small
harbo
break
on th
natur
with
is abs
re 5.10 illus
re 5.9 as sou
re 5.10 The
above incid
ibuted spectr
ess, however
us frequency
l to prevent
or oscillation
king wave is
he south and
ral condition
different po
sorbed and th
strates the i
uth source, an
incident wav
dent wave is
rum in a giv
r we can use
y of long w
overtopping
n itself. Sin
negligible.
d west side,
n as much as
orosity, based
he incident w
ncident wav
nd along the
ve for white
s an idealiz
ven frequenc
e this wave
waves. The am
g or inundatio
nce the wav
Sponge laye
, and the pa
s possible. D
d on its char
wave interac
ves. They a
grey line in
e noise analy
zed profile,
cy range. It
train as a to
mplitude of
on. So that,
ves have lon
er is defined
artially refle
Different seg
racter and te
cts with coas
are applied a
n Figure 5.9 a
ysis in LA/LB
which is ge
is not what
ool to inspe
f incident wa
the simulati
ng period (
along the ex
ective coastl
gment along
exture. Ther
stline as in th
along the o
as west sour
B port
enerated fro
t happened i
ct harbor be
ave is set to
ion is concen
≥ 12 min),
xterior bound
line is set t
the coastlin
efore, the ra
he nature.
10
range line i
rce.
om uniforml
in the natura
ehavior unde
be relativel
ntrated on th
the issue o
dary of ocea
to imitate th
ne is assigne
adiated wave
8
in
ly
al
er
ly
he
of
an
he
ed
es
5
F
The a
surfa
result
60.7
oscill
5.2.2 Result
Figure 5.11
Figure 5.12
above curves
ce elevation
t into spectr
minutes and
lation than fr
ts
The predic
The predicte
s are the num
n along time
al density di
d the same in
from west sou
ted response
ed response
merical solut
e at the star
istribution a
ncident wave
urce.
e at tidal stat
at tidal statio
tion at the lo
location in
as in Fig 5.1
e from south
tion in LA/L
on in LA/LB
ocation of tid
Fig 5.9. Tra
3. The reson
h source wou
LB port (sout
B port (west
dal gauge, so
ansform the
nant mode i
uld induce m
10
th source)
source)
o they predic
time domai
s at period o
more intensiv
9
ct
in
of
ve
Figur
wave
water
To as
adopt
tidal
dimen
chara
harbo
facin
ratio
The a
Figure
re 5.13 is th
e frequency.
r depth at the
scertain this
ted mild-slo
gauge statio
nsionless va
acteristic wav
or. In this ca
g coastal lin
of the wave
advantage o
6
e 5.13 Spect
he spectra of
It shows th
e tidal gauge
result, it is
ope equation
on as in Fig
ariable kl, wh
velength of
ase, l is take
ne. The y ax
e amplitude
f dimension
60.7 min
53.3 min
tra of oscillat
f white-noise
hat the reson
e station is 2
necessary t
to analyze
gure 5.14. I
here k =
ଶగ
i
incoming w
en as the seg
xis represent
at the tidal g
nless respons
34.1 min
tion in LA/L
e analysis, a
nant mode o
.0 m.
to review pr
LA/LB port
n the respon
is the wave n
waves, and l s
gment betwe
s the amplif
gauge to the
se curve is t
26 min
LB port
and the vari
f LA/LB po
revious work
t, and acquir
nse curve, t
number. The
stands for th
een the outer
fication facto
e wave ampl
that the labo
able in hori
ort is 60.7 m
k. The Xing
res the respo
the x axis r
e symbol L r
he characteri
r harbor entr
or R, which
litude outsid
oratory mod
11
zontal axis
minutes, whe
g et al. (2012
onse curve a
represents th
represents th
istic length o
rance and th
is defined a
de the harbo
el can follow
0
is
en
2)
at
he
he
of
he
as
or.
w
the s
small
nume
the F
close
mode
oscill
ame curves
ler water ba
erical analys
Figure 5.14,
to the 60.7
el), and this
lation of LA
Figure 5
as the real
asin can be d
sis with mild
which show
7 minutes fro
indicates th
A/LB port.
.14 Amplifi
60 min
harbor do.
designed, wh
d-slope equa
ws that the f
om present
hat the nonli
fication facto
26.3
With the he
hich can sav
ation (linear
first resonan
study with B
inearity doe
or at tidal gau
min
elp of this c
ve much res
r model), Xi
nt mode is 6
Boussinesq-
es not appea
uge with res
curve, the ex
search fundi
ing et al. (20
60 minutes.
-type equatio
ar to be sign
spect to kl
18.0 min
11
xperiments i
ing. After th
012) acquire
This result
on (nonlinea
nificant in th
1
in
he
es
is
ar
he
5.3 S
San D
betwe
5.15,
locati
Unite
and n
indic
Figur
(a).
(c).
San Diego H
Diego harbo
een the Unit
and the ye
ion of San
ed States, an
nearby shore
ates the loca
re 5.15 (a) S
Harbor, Cali
or is located
ted States an
ellow star in
Diego harbo
nd it’s at the
eline. The (c
ation of tidal
San Diego ha
ifornia
d on the sout
nd Mexico.
ndicates the
or. The (a)
south end o
c) is the bird
l gauge.
arbor on the
th end of C
The location
tidal gauge
shows the h
f the west co
d view of Sa
West Coast
(b).
alifornia, an
n and layout
e location. F
harbor (as t
oast. The (b)
an Diego ha
t; (b) & (c) Z
nd it’s near
t are shown
Figure 5.15
the red pin
) illustrates t
arbor, and th
Zoom-in; (Go
11
to the borde
in the Figur
describes th
mark) in th
the outer are
he yellow sta
oogle maps)
2
er
re
he
he
ea
ar
)
5
For th
spatia
mark
the ge
Figur
The r
(380×
coeff
by ca
simul
5.3.1 Model
he present st
al discretiza
ks the genera
eneration bo
re 5.16 The
resolution h
×420) cells.
ficient B is 1
alibrating the
lation of 48
l Setup
tudy, the bat
ation, one di
ation bounda
oundary of in
layout and b
has been def
The time st
1/15. B is an
e consequent
hours costs
thymetry of
igital map f
ary of incom
ncoming wav
bathymetry o
fined as 40
tep Δt is 1.2
n arbitrary c
t linear dispe
approx. 2 h
San Diego h
file is acquir
ming waves f
ves from we
of San Diego
m ( Δx) by
2 s, Courant
constant in E
ersion relatio
ours of com
harbor is use
red as Figur
from south,
est. Tidal stat
o harbor on m
y 40 m ( Δy)
number is 0
Eq. 3.15~Eq
on with Stok
mputer work,
ed in the sim
re 5.16. The
and the grey
ation is mark
mean tidal le
), and there
0.631, and t
. 3.17, and i
kes first orde
and Table 4
11
mulation. Afte
e orange lin
y line denote
ked by star.
evel (MTL)
e are 159,60
the dispersio
is determine
er theory. Th
4.1 shows th
3
er
ne
es
00
on
ed
he
he
confi
They
line i
The
distri
proce
vario
small
harbo
break
on th
natur
with
is abs
guration of
y are applied
n Figure 5.1
Figure 5.17
above incid
ibuted spectr
ess, however
us frequency
l to prevent
or oscillation
king wave is
he south and
ral condition
different po
sorbed and th
the comput
along the or
6 as west so
7 The incide
dent wave is
rum in a giv
r we can use
y of long w
overtopping
n itself. Sin
negligible.
d west side,
n as much as
orosity, based
he incident w
tational pow
range line in
ource.
ent wave for
s an idealiz
ven frequenc
e this wave
waves. The am
g or inundatio
nce the wav
Sponge laye
, and the pa
s possible. D
d on its char
wave interac
wer. Figure
n Figure 5.16
r white noise
zed profile,
cy range. It
train as a to
mplitude of
on. So that,
ves have lon
er is defined
artially refle
Different seg
racter and te
cts with coas
5.17 illustr
6 as south so
e analysis in
which is ge
is not what
ool to inspe
f incident wa
the simulati
ng period (
along the ex
ective coastl
gment along
exture. Ther
stline as in th
rates the inc
ource, and a
San Diego h
enerated fro
t happened i
ct harbor be
ave is set to
ion is concen
≥ 12 min),
xterior bound
line is set t
the coastlin
efore, the ra
he nature.
11
cident wave
along the gre
harbor
om uniforml
in the natura
ehavior unde
be relativel
ntrated on th
the issue o
dary of ocea
to imitate th
ne is assigne
adiated wave
4
s.
ey
ly
al
er
ly
he
of
an
he
ed
es
5
Fig
Fi
The a
surfa
result
273 m
magn
5.3.2 Result
gure 5.18 Th
igure 5.19 T
above curves
ce elevation
t into spectr
minutes and
nitude of inte
ts
he predicted
The predicted
s are the num
n along time
al density di
d the same
ensive oscill
d response at
d response at
merical solut
at the star l
istribution a
incident wa
ation as from
t tidal station
t tidal station
tion at the lo
ocation in F
as in Fig 5.2
ave from so
m west sourc
n in San Dieg
n in San Die
ocation of tid
Fig 5.16. Tr
0. The reson
outh source
ce.
go harbor (s
ego harbor (w
dal gauge, so
ansform the
nant mode i
would indu
11
outh source)
west source)
o they predic
e time domai
s at period o
uce the sam
5
)
)
ct
in
of
me
Figur
wave
when
To as
adopt
at tid
dimen
chara
harbo
facin
ratio
The a
re 5.20 is th
e frequency.
n water depth
scertain this
ted mild-slo
dal gauge sta
nsionless va
acteristic wav
or. In this ca
g coastal lin
of the wave
advantage o
Figure 5.20
he spectra of
It shows th
h at the tidal
result, it is
pe equation
ation as in F
ariable kl, wh
velength of
ase, l is take
ne. The y ax
e amplitude
f dimension
273 min
81.9 min
0 Spectra of
f white-noise
hat the reson
gauge statio
necessary t
to analyze
Figure 5.21.
here k =
ଶగ
i
incoming w
en as the seg
xis represent
at the tidal g
nless respons
58.5 min
26
30 min
f oscillation
e analysis, a
nant mode o
on is 2.0 m.
to review pr
San Diego p
In the respo
is the wave n
waves, and l s
gment betwe
s the amplif
gauge to the
se curve is t
6.9 min
25.6 min
n
23.8 min
21 m
in San Dieg
and the vari
of San Dieg
revious work
port, and acq
onse curve,
number. The
stands for th
een the outer
fication facto
e wave ampl
that the labo
min
13.9 mi
o harbor
able in hori
o harbor is
k. The Xing
quires the re
the x axis r
e symbol L r
he characteri
r harbor entr
or R, which
litude outsid
oratory mod
in
13.2 min
11
zontal axis
273 minute
g et al. (2012
esponse curv
represents th
represents th
istic length o
rance and th
is defined a
de the harbo
el can follow
6
is
s,
2)
ve
he
he
of
he
as
or.
w
the s
small
nume
the F
close
mode
oscill
ame curves
ler water ba
erical analys
Figure 5.21,
to the 273
el), and this
lation of San
Figure 5
275
as the real
asin can be d
sis with mild
which show
minutes fro
indicates th
n Diego harb
5.21 Amplif
86 min
min
harbor do.
designed, wh
d-slope equa
ws that the fi
om present
hat the nonli
bor.
fication facto
58 min
37 m
With the he
hich can sav
ation (linear
irst resonant
study with B
inearity doe
or at tidal ga
min
34 min
elp of this c
ve much res
r model), Xi
t mode is 27
Boussinesq-
es not appea
auge with res
24.2 min
curve, the ex
search fundi
ing et al. (20
75 minutes.
-type equatio
ar to be sign
spect to kl
16.
11
xperiments i
ing. After th
012) acquire
This result
on (nonlinea
nificant in th
8 min
7
in
he
es
is
ar
he
5.4 P
The n
Amer
is on
Pago
to the
of Pa
Figur
(a).
(c).
Pago Pago H
naturally for
rican Samoa
n the northw
harbor. The
e northeast o
ago Pago har
re 5.22 (a) P
Harbor, Am
rmed Pago P
a in southern
west coast in
e (a) shows t
of Australia.
rbor, and the
Pago Pago h
merican Sam
Pago harbor
n Pacific Oce
side the har
the harbor (a
The (b) illu
e yellow star
harbor in the
moa
is located o
ean. The cap
rbor. Figure
as the red pin
ustrates the w
indicates th
South Pacif
(b).
on the south
ptital of Ame
5.15 descri
n mark) in t
whole island
he location of
fic; (b) & (c)
side of Tut
erican Samoa
ibes the loca
the Pacific o
d. The (c) is
f tidal gauge
) Zoom-in; (
11
tuila island o
a, Pago Pago
ation of Pag
ocean, and it
the bird view
e
(Google map
8
of
o,
go
’s
w
ps)
5
For th
spatia
mark
the ge
Figur
The r
(610×
coura
const
dispe
1 hou
powe
5.4.1 Model
he present st
al discretiza
ks the genera
eneration bo
re 5.23 The
resolution h
×410) cells
ant number
tant in Eq. 3
ersion relatio
ur of compu
er.
l Setup
tudy, the bat
ation, one di
ation bounda
oundary of in
layout and b
has been def
in the abov
is 0.735, a
3.15~Eq. 3.
on with Stoke
uter work, a
thymetry of P
igital map f
ary of incom
ncoming wav
bathymetry o
fined as 10
ve model. In
nd the disp
17, and is d
es first order
nd Table 4.
Pago Pago h
file is acquir
ming waves f
ves from eas
of Pago Pago
m ( Δx) by
n the presen
persion coeff
determined b
r theory. The
1 shows the
harbor is use
red as Figur
from south,
st. Tidal stat
o harbor on
y 10 m ( Δy)
nt model, th
fficient B is
by calibratin
e simulation
e configurat
ed in the sim
re 5.23. The
and the grey
tion is marke
mean tidal l
), and there
he time step
s 1/15. B is
ng the cons
n of 15 hours
ion of the c
11
mulation. Afte
e orange lin
y line denote
ed by star.
evel (MTL)
e are 250,10
p Δt is 0.5
s an arbitrar
sequent linea
s costs appro
computationa
9
er
ne
es
00
s,
ry
ar
ox.
al
Whit
Figur
Figur
The
distri
proce
vario
small
harbo
break
on th
natur
with
is abs
e noise ana
re 5.24 illus
re 5.23 as so
Figure 5.24
above incid
ibuted spectr
ess, however
us frequency
l to prevent
or oscillation
king wave is
he south and
ral condition
different po
sorbed and th
alysis is con
strates the i
uth source, a
4 The incide
dent wave is
rum in a giv
r we can use
y of long w
overtopping
n itself. Sin
negligible.
d west side,
n as much as
orosity, based
he incident w
nducted in th
ncident wav
and along th
ent wave for
s an idealiz
ven frequenc
e this wave
waves. The am
g or inundatio
nce the wav
Sponge laye
, and the pa
s possible. D
d on its char
wave interac
he numerica
ves. They a
he grey line i
r white noise
zed profile,
cy range. It
train as a to
mplitude of
on. So that,
ves have lon
er is defined
artially refle
Different seg
racter and te
cts with coas
al model of
are applied a
in Figure 5.2
e analysis in
which is ge
is not what
ool to inspe
f incident wa
the simulati
ng period (
along the ex
ective coastl
gment along
exture. Ther
stline as in th
f Pago Pago
along the o
23 as west so
Pago Pago h
enerated fro
t happened i
ct harbor be
ave is set to
ion is concen
≥ 12 min),
xterior bound
line is set t
the coastlin
efore, the ra
he nature.
12
o harbor, an
range line i
ource.
harbor
om uniforml
in the natura
ehavior unde
be relativel
ntrated on th
the issue o
dary of ocea
to imitate th
ne is assigne
adiated wave
0
nd
in
ly
al
er
ly
he
of
an
he
ed
es
5
F
F
The a
be th
the ti
is at p
the sa
5.4.2 Result
igure 5.25 T
Figure 5.26
above curve
he predicted
me domain r
period of 20
ame magnitu
ts
The predicte
The predicte
s are the num
surface elev
result into sp
0.2 minutes a
ude of intens
ed response a
ed response
merical solu
vation along
pectral densi
and the same
sive oscillati
at tidal statio
at tidal statio
ution at the l
time at the
ity distributi
e incident w
on as from e
on in Pago P
on in Pago P
location of ti
star locatio
ion as in Fig
wave from so
east source.
Pago harbor
Pago harbor
idal gauge,
n in Fig 5.2
5.27. The re
outh source w
12
(south sourc
(east source
so this woul
23. Transform
esonant mod
would induc
1
ce)
e)
ld
m
de
ce
Figur
wave
when
To as
adopt
curve
the di
the ch
of ha
facin
ratio
The a
re 5.27 is th
e frequency.
n water depth
scertain this
ted mild-slo
e at tidal gau
imensionles
haracteristic
rbor. In this
g coastal lin
of the wave
advantage o
Figure 5.27
he spectra of
It shows th
h at the tidal
result, it is
ope equation
uge station a
s variable kl
wavelength
case, l is tak
ne. The y ax
e amplitude
f dimension
Spectra of
f white-noise
hat the reson
gauge statio
necessary t
n to analyze
as in Figure 5
l, where k =
h of incoming
ken as the se
xis represent
at the tidal g
nless respons
22.8 min
oscillation i
e analysis, a
nant mode o
on is 1.2 m.
to review pr
e Pago Pago
5.28. In the
ଶగ
is the wa
g waves, and
egment betw
s the amplif
gauge to the
se curve is t
17
20.2 min
n
in Pago Pago
and the vari
f Pago Pago
revious work
o harbor, an
response cu
ave number.
d l stands fo
ween the oute
fication facto
e wave ampl
that the labo
7.6 min
o harbor
able in hori
o harbor is 2
k. Huang an
nd acquires
urve, the x ax
The symbo
r the charact
er harbor ent
or R, which
litude outsid
oratory mod
12
zontal axis
20.2 minute
nd Lee (2012
the respons
xis represent
l L represent
teristic lengt
trance and th
is defined a
de the harbo
el can follow
2
is
s,
2)
se
ts
ts
th
he
as
or.
w
the s
small
nume
acqui
result
(nonl
ame curves
ler water ba
erical analys
ire the Figur
t is close to
linear model
Figure 5
18 min
as the real
asin can be d
sis with mi
re 5.28, wh
o the 20.2 m
l).
.28 Amplifi
n
9 min
harbor do.
designed, wh
ild-slope eq
ich shows t
minutes from
fication facto
4.7 mi
With the he
hich can sav
uation (line
hat the first
m present st
or at tidal gau
n
elp of this c
ve much res
ear model),
t resonant m
tudy with B
uge with res
curve, the ex
search fundi
Huang and
mode is 18 m
Boussinesq-t
spect to kl
2.5 min
2
12
xperiments i
ing. After th
d Lee (2012
minutes. Th
type equatio
2.4 min
3
in
he
2)
is
on
124
5.5 Summary
In this chapter, the real harbor bathymetry and layout are concerned, and the present
numerical model is applied into four harbors on Pacific coasts, including three harbors in
California and one harbor in American Samoa. This preliminary study is dedicated to
further verify the present numerical model in a realistic condition, and to ascertain the
earlier study. The fundamental frequencies of the four subject harbors are ascertained.
The reference study adopted the Berkhoff equation, therefore the weakly nonlinear terms
in the Boussinesq equations are used to complement the earlier work as well. Through
comparison, the nonlinearity does not appear to be significant in the harbor oscillation,
but the effect to the resonant mode is observable in smaller harbors.
Another point of concern is the incoming wave direction, which impacts the resonance
intensity through the harbor’s orientation and layout. For Crescent City harbor and Los
Angeles/Long Beach ports, both the steady state and transient state analysis pointed out
that the incident waves from south induce bigger oscillation than from west side. This is
because these two harbor both open to the south side, with breakwater block the other
directions. It is noticed that the Mild-slope model is based on steady state and the
Boussinesq-type model is based on transient state. This is possible reason that the gap
between south source and west source is bigger in the Boussinesq model than in Berkhoff
model. The incident wave direction does not impact very much in San Diego and Pago
Pago harbor, this is because San Diego has a hook-like layout and Pago Pago harbor is
facing the southeast with a bending layout. Besides, they have no breakwater outside
entrance, and these factors prevent the harbor from being more sensitive to a certain
direction.
125
CHAPTER 6: FLUCTUATING TIDAL LEVEL AND VARYING HARBOR LAYOUT
In last chapter, we focused on the unchanged mean tidal level (MTL), which does not
represent the practical situation. In this chapter, we will focus on studying harbor
oscillation with fluctuating tidal level and the accompanying changes in harbor layout
(due to the varying water depth).
As widely known, the sea level is moving up and down periodically due to the
varying attractive forces of the celestial bodies moon, un and earth, etc. This commonly
seen phenomenon in the nature significantly impacts on the harbor oscillation, especially
when the time span gets long enough. Through a whole tidal period, the sea surface
slowly moves up and down between low and high tidal levels. Since the water surface
level is not constant, some near shore area will be exposed to the air during low tide, and
will be submerged again on high tidal level. Therefore, the shoreline between seawater
and land slowly moves back and forth, and the seawater area expands and shrinks. Due to
the irregular bathymetry of real harbors, the harbor layout changes irregularly as well.
This factor eventually alters the pattern of harbor oscillation, when a strong tsunami is
impacting with a long time span. The upcoming sections will review two major tsunamis
in recent years, and analyze the potential factors that contributes to the unusual oscillation
behavior in three Californian harbors.
6.1 O
Xing
Cresc
and M
Figur
Observed Ph
, et al. (2012
cent City ha
Mar. 11
th
, 20
re 6.1 Water
henomenon
2) noticed th
arbor oscillat
011 Tohoku e
r level witho
n in Reality
hat unusually
tion during
earthquake-t
out tidal effe
y more reso
the Feb. 27
tsunami as sh
ect in historic
nant modes
7
th
, 2010 Ch
hown in Fig
cal tsunamis
occur in the
hilean earthq
g 6.1~Fig 6.2
s (Xing, et. a
12
e spectrum o
quake-tsunam
2.
al (2012))
6
of
mi
Figur
Cresc
The r
re 6.2 Spect
cent City har
reason is the
tra of the cor
rbor shows m
large ampli
rresponsive c
more resona
tude of tidal
cases in Cres
nt modes tha
l fluctuation
scent City h
an usual, in
during the i
arbor (Xing,
2010 and 20
impact time.
12
, et. al (2012
011 tsunami
7
2)
s.
This
2010
Figur
phenomeno
and 2011 ts
re 6.3 Water
n is not obs
sunamis show
r level witho
served in Lo
w the same r
out tidal effe
os Angeles/L
resonant mod
ect in historic
Long Beach
de as usual,
cal tsunamis
h Port, and t
see Fig 6.3~
s (Xing, et. a
12
the spectra i
~Fig 6.4.
al (2012))
8
in
Figur
LA/L
becau
re 6.4 Spect
LB port show
use the tidal
tra of the cor
ws the same
fluctuation d
rresponsive c
fundamenta
during the im
cases in LA/
al frequency
mpact time d
/LB port (Xi
in 2010 and
did not alter
ing, et. al (20
d 2011 tsuna
the harbor la
12
012)
amis as usua
ayout.
9
al,
Addit
durin
to sho
Figur
tionally, Xin
ng Feb. 27
th
,
orter period.
re 6.5 Water
ng et. al (20
2010 Chile
The altered
r level witho
12) reports t
an tsunami
d harbor layo
out tidal effe
that fundame
and Mar. 11
out and bathy
ect in historic
ental frequen
1
th
, 2011 To
ymetry are th
cal tsunamis
ncy in San D
ohoku tsunam
he possible r
s (Xing, et. a
13
Diego harbo
mi shift dow
reasons.
al (2012))
0
or,
wn
Figur
As sh
event
2011
re 6.6 Spect
hown in the
t of 2010 sh
tsunami eve
tra of the cor
e above figu
hifts from 27
ent shifts fro
rresponsive c
ures, the str
70 min dow
om 270 min d
cases in San
ronger reson
wn to 57.8 m
down to 34.4
n Diego harb
nant period
min, and the
4 min.
or (Xing, et.
observed in
strong reson
13
. al (2012)
n the tsunam
nant mode i
1
mi
in
132
6.2 Possible Factors
The factors that could affect the fundamental frequency of a harbor can be categorized as
characteristics of harbor and natural forces, and they are shown in Table 6.1.
Table 6.1 Factors that affects the fundamental frequency of a harbor
Characteristics of Harbor Natural Forces
1. bathymetry
overall water depth
underwater topography
1. tide
sea surface elevation
2. harbor layout
shape of coastline
area of seawater
boundary condition
2. spectral density of incident wave
input energy
3. harbor orientation
direction of harbor trend
opening direction
breakwater
Harbor bathymetry and layout are both affected by tidal fluctuation. A harbor on different
tidal levels might have different fundamental frequencies, because the altered bathymetry
exerts influence through dispersion relation and the changed layout exhibits itself by the
sea area as well as boundary conditions. In addition, the spectral content of incident
waves is another important external factors in reality, for its irregular nature. Therefore,
this chapter will work on these possible factors to determine the reasons that lead to the
described phenomena of concern.
6.3 W
6
As th
differ
Table
Tida
For e
ideali
same
F
White Noise
6.3.1 Cresce
he first step,
rent tidal lev
e 6.2 Chosen
al Level
1
2
3
4
5
each of the
ized inciden
for all the f
igure 6.7 Th
e Analysis o
ent City Ha
, it is interes
vels as shown
n tidal levels
W
ex
mean lo
mean ti
mean hi
ext
tidal levels
nt wave train
five tidal leve
he incident w
n Separate
arbor
sting to inve
n in Table 6
s of Crescen
Water Levels
xtremely low
ow water (M
idal level (M
igh water (M
tremely high
above, a n
n as in Figu
els, their am
wave for wh
Tidal Level
estigate the b
.2.
nt City harbo
w
MLW)
MTL)
MHW)
h
numerical m
ure 6.7. Whi
mplitudes are
hite noise ana
ls
behavior of
or
D
model is buil
ile the shape
scaled to eq
alysis in Cre
f Crescent C
Depth at Sta
0.8 m
1.5 m
2.3 m
3.0 m
3.6 m
lt and simul
e of inciden
qualize nonli
escent City h
13
City harbor o
ation
lated with a
nt wave is th
inearity.
harbor
3
on
an
he
Tidal
For th
After
mark
the ge
Figur
The r
The t
appro
comp
as ma
l Level 1:
he present s
r spatial disc
ks the genera
eneration bo
re 6.8 The la
resolution is
time step Δt
ox. 90 minu
putational po
arked by star
study, the ba
cretization, o
ation bounda
oundary of in
ayout and ba
defined as 9
is 0.4 s, and
utes of comp
ower. Figure
r in Figure 6
athymetry of
one digital m
ary of incom
ncoming wav
athymetry of
9 m ( Δx) by
d Courant nu
puter work,
e 6.9~6.10 ill
6.8, and Figu
l
f Crescent C
map file is ac
ming waves f
ves from we
f Crescent C
9 m ( Δy), an
umber is 0.6
and Table
lustrate the n
ure 6.11 show
City harbor i
cquired as Fi
from south,
est. Tidal stat
City harbor on
nd there are
638. The sim
4.1 shows
numerical so
ws the corre
is used in th
igure 6.8. Th
and the grey
ation is mark
n extremely
127,300 (33
mulation of 2
the configu
olution at th
sponding sp
13
he simulation
he orange lin
y line denote
ked by star.
low tide
35×380) cell
24 hours cost
uration of th
e tidal statio
pectral densit
4
n.
ne
es
s.
ts
he
on
ty.
F
F
Figur
Figure 6.9 P
Figure 6.10
re 6.11 Spec
Predicted res
Predicted re
ctral density
sponse at tid
esponse at tid
distribution
25.4
dal station wi
dal station w
n of Crescent
min
22.8 min
21.8 min
19.8 min
18.2 m
ith extremely
with extremel
t City harbor
min
15.2 min
y low tide (s
ly low tide (
r with extrem
13
south source
(west source
mely low tid
5
e)
)
de
Tidal
For th
By sp
mark
the ge
Figur
The r
The t
appro
comp
mark
l Level 2:
he present s
patial discret
ks the genera
eneration bo
re 6.12 The
resolution is
time step Δt
ox. 90 minu
putational po
ked by the sta
study, the ba
tization, one
ation bounda
oundary of in
layout and b
defined as 9
is 0.4 s, and
utes of comp
ower. Figure
ar in Figure
athymetry of
e digital map
ary of incom
ncoming wav
bathymetry o
9 m ( Δx) by
d Courant nu
puter work,
e 6.13~6.14 i
6.12, and Fi
l
f Crescent C
p file is acqu
ming waves f
ves from we
of Crescent C
9 m ( Δy), an
umber is 0.6
and Table
illustrate the
gure 6.15 sh
City harbor i
uired as Figu
from south,
est. Tidal stat
City harbor
nd there are
638. The sim
4.1 shows
e numerical s
hows the spe
is used in th
ure 6.12. Th
and the grey
ation is mark
on mean low
127,300 (33
mulation of 2
the configu
solution at ti
ectral density
13
he simulation
he orange lin
y line denote
ked by star.
w water
35×380) cell
24 hours cost
uration of th
idal station a
y distribution
6
n.
ne
es
s.
ts
he
as
n.
F
F
Fig
Figure 6.13
Figure 6.14
gure 6.15 Sp
Predicted re
Predicted re
pectral densit
esponse at ti
esponse at tid
ty distributio
25.4 min
22.8
idal station w
dal station w
on of Cresce
n
8 min
21.4 min
19.8 min
18.2
with mean lo
with mean low
ent City harb
min
13.3
ow water (so
w water (we
bor with mea
min
13
outh source)
est source)
an low tide
7
Tidal
For th
By sp
mark
the ge
Figur
The r
The t
appro
comp
mark
l Level 3:
he present s
patial discret
ks the genera
eneration bo
re 6.16 The
resolution is
time step Δt
ox. 90 minu
putational po
ked by the sta
study, the ba
tization, one
ation bounda
oundary of in
layout and b
defined as 9
is 0.4 s, and
utes of comp
ower. Figure
ar, and Figur
athymetry of
e digital map
ary of incom
ncoming wav
bathymetry o
9 m ( Δx) by
d Courant nu
puter work,
e 6.17~6.18 i
re 6.19 show
l
f Crescent C
p file is acqu
ming waves f
ves from we
of Crescent C
9 m ( Δy), an
umber is 0.6
and Table
illustrate the
ws the corres
City harbor i
uired as Figu
from south,
est. Tidal stat
City harbor
nd there are
638. The sim
4.1 shows
e numerical s
sponding spe
is used in th
ure 6.16. Th
and the grey
ation is mark
on mean tida
127,300 (33
mulation of 2
the configu
solution at ti
ectral densit
13
he simulation
he orange lin
y line denote
ked by star.
al level
35×380) cell
24 hours cost
uration of th
idal station a
ty distributio
8
n.
ne
es
s.
ts
he
as
on.
F
F
Fig
Figure 6.17
igure 6.18 P
gure 6.19 Sp
Predicted re
Predicted res
pectral densit
esponse at tid
sponse at tid
ty distributio
2
22.8
25.4 m
dal station w
dal station wi
on of Cresce
19.8 min
18.2
21.8 min
8 min
min
with mean tid
ith mean tida
ent City harb
min
16.5
min
15.2
min
13
m
dal level (sou
al level (wes
bor with mea
3.3
min
12.6
min
13
uth source)
st source)
an tidal level
9
l
Tidal
For th
By sp
mark
the ge
Figur
The r
The t
appro
comp
mark
l Level 4:
he present s
patial discret
ks the genera
eneration bo
re 6.20 The
resolution is
time step Δt
ox. 90 minu
putational po
ked by the sta
study, the ba
tization, one
ation bounda
oundary of in
layout and b
defined as 9
is 0.4 s, and
utes of comp
ower. Figure
ar, and Figur
athymetry of
e digital map
ary of incom
ncoming wav
bathymetry o
9 m ( Δx) by
d Courant nu
puter work,
e 6.21~6.22 i
re 6.23 show
l
f Crescent C
p file is acqu
ming waves f
ves from we
of Crescent C
9 m ( Δy), an
umber is 0.6
and Table
illustrate the
ws the corres
City harbor i
uired as Figu
from south,
est. Tidal stat
City harbor
nd there are
638. The sim
4.1 shows
e numerical s
sponding spe
is used in th
ure 6.20. Th
and the grey
ation is mark
on mean hig
127,300 (33
mulation of 2
the configu
solution at ti
ectral densit
14
he simulation
he orange lin
y line denote
ked by star.
gh water
35×380) cell
24 hours cost
uration of th
idal station a
ty distributio
0
n.
ne
es
s.
ts
he
as
on.
F
F
Figu
Figure 6.21
igure 6.22 P
ure 6.23 Spe
Predicted re
Predicted res
ectral density
esponse at tid
sponse at tid
y distributio
25.4 m
32.1 min
dal station w
dal station wi
on of Crescen
18.2
20.0 min
21.8 min
22.8 min
min
with mean hig
ith mean hig
nt City harbo
min
gh water (so
gh water (we
or with mean
14
outh source)
est source)
n high water
1
r
Tidal
For th
By sp
mark
the ge
Figur
The r
The t
appro
comp
mark
l Level 5:
he present s
patial discret
ks the genera
eneration bo
re 6.24 The
resolution is
time step Δt
ox. 90 minu
putational po
ked by the sta
study, the ba
tization, one
ation bounda
oundary of in
layout and b
defined as 9
is 0.4 s, and
utes of comp
ower. Figure
ar, and Figur
athymetry of
e digital map
ary of incom
ncoming wav
bathymetry o
9 m ( Δx) by
d Courant nu
puter work,
e 6.25~6.26 i
re 6.27 show
l
f Crescent C
p file is acqu
ming waves f
ves from we
of Crescent C
9 m ( Δy), an
umber is 0.6
and Table
illustrate the
ws the corres
City harbor i
uired as Figu
from south,
est. Tidal stat
City harbor
nd there are
638. The sim
4.1 shows
e numerical s
sponding spe
is used in th
ure 6.24. Th
and the grey
ation is mark
on extremely
127,300 (33
mulation of 2
the configu
solution at ti
ectral densit
14
he simulation
he orange lin
y line denote
ked by star.
y high tide
35×380) cell
24 hours cost
uration of th
idal station a
ty distributio
2
n.
ne
es
s.
ts
he
as
on.
Fi
Fig
Figur
igure 6.25 P
gure 6.26 Pr
re 6.27 Spec
Predicted resp
redicted resp
tral density d
ponse at tida
ponse at tida
distribution
22.8
25.4 mi
32.1 min
al station wit
al station with
of Crescent
18.2
19.8 min
21.8 min
8 min
in
th extremely
h extremely
City harbor
min
y high tide (s
high tide (w
with extrem
14
south source
west source)
mely high tid
3
e)
de
Integ
oscill
harbo
the F
The t
and th
woul
openi
grate the wa
lation R by
or sensitivity
igure 6.28 is
Figure 6.2
tidal levels in
he most inte
d induce stro
ing to the so
ave spectrum
the incident
y on a given
s acquired as
28 The sensi
n the above
ensive respon
onger oscilla
outh, and blo
m by freque
t wave energ
n tidal level.
s follow.
itivity of Cre
curves are in
nse occurs o
ation than th
cking the we
ency and div
gy I. The ra
Repeat the
escent City h
ndicated by
on 1.2 m. Th
he ones of w
est.
vide the res
atio R/I can
same proce
harbor on va
the water de
he incident w
west source, b
sulting ener
be used to
ess for all th
arious tidal le
epth at tidal
waves comin
because the
14
rgy of harbo
represent th
he tide level
evels
gauge statio
ng from sout
breakwater
4
or
he
s,
on,
th
is
To as
analy
respo
axis r
L rep
chara
harbo
6.16,
which
incid
6.29
repre
scertain the
yze Crescent
onse curves
represents th
presents the
acteristic len
or entrance a
Figure 6.2
h is defined
ent wave. A
shows that
sentative tid
(a).
solution of p
t City harbo
at tidal stati
he dimension
e characteris
ngth of harbo
and the facin
0, and Figu
as ratio of t
After numeric
the first res
dal levels and
present stud
or with mean
ion are show
nless wave n
stic wavelen
or. In this ca
ng coastal li
ure 6.24. Th
the wave am
cal analysis
onant mode
d the corresp
dy, Xiuying X
n low tide,
wn as Figure
number kl, w
ngth of inco
ase, l is take
ine, as show
he y axis re
mplitude at th
with mild-s
in kl is fair
ponsive harb
Xing adopte
mean tide, a
e 6.29. In th
where k =
ଶగ oming wave
en as the se
wn in Figure
epresents the
he tidal gaug
slope equatio
rly constant
bor layouts.
ed mild-slop
and mean h
he response
is the wave
es, and l st
egment betw
e 6.8, Figure
e amplificat
ge to the amp
on (linear m
t in response
14
pe equation t
high tide. Th
curves, the
number. Th
tands for th
ween the oute
e 6.12, Figur
tion factor R
mplitude of th
model), Figur
e of the thre
5
to
he
x
he
he
er
re
R,
he
re
ee
Fi
(b
When
for lo
soluti
mode
level
(b).
igure 6.29 (a
b) Response c
n taking cor
ow tide, 22 m
ion by prese
es are 25.4 m
three, 25.4 m
a) Response
curves in ter
rresponding
min for mean
ent Boussin
min for tida
min for tidal
20 min
22 min
25 min
11.5 mi
curves in te
rm of freque
l for differen
n tide, and 2
esq-type equ
al level one,
l level four, a
in
10.3 min
erm of kl at ti
ncy at tidal g
nt layouts, t
25 min for hi
uation (nonl
21.4 min fo
and 22.8 min
9 min
tide gauge fo
gauge for di
the primary
igh tide. Thi
linear mode
or tidal leve
n for tidal le
or different t
ifferent tidal
resonant mo
is result is co
el), and prim
el two, 19.8
evel five.
3.8 min
14
idal level
level
ode is 20 mi
onsistent wit
mary resonan
min for tida
6
in
th
nt
al
6
As th
Port o
Table
Tida
For e
ideali
same
F
6.3.2 Los A
he first step,
on different
e 6.3 Chosen
al Level
1
2
3
4
5
each of the
ized inciden
for all the f
igure 6.30 T
ngeles/Long
it is interes
tidal levels a
n tidal levels
W
ex
mean lo
mean ti
mean hi
ext
tidal levels
nt wave train
five tidal leve
The incident
g Beach Por
ting to inves
as shown in
s of Los Ang
Water Levels
xtremely low
ow water (M
idal level (M
igh water (M
tremely high
above, a n
n as in Figur
els, their am
t wave for w
rt
stigate the b
Table 6.3.
geles/Long B
w
MLW)
MTL)
MHW)
h
numerical m
re 6.30. Wh
mplitudes are
white noise an
behavior of L
Beach Port
D
model is buil
hile the shap
scaled to eq
nalysis in LA
Los Angeles
Depth at Sta
1.0 m
1.5 m
2.0 m
2.6 m
3.0 m
lt and simul
e of inciden
qualize nonli
A/LB Port
14
s/Long Beac
ation
lated with a
nt wave is th
inearity.
7
ch
an
he
Tidal
For t
spatia
mark
the ge
Figur
The r
cells.
simul
confi
the n
nume
show
l Level 1:
the present
al discretiza
ks the genera
eneration bo
re 6.31 The
resolution is
In the pres
lation of 72
guration of
numerical m
erical solutio
ws the corresp
study, the b
ation, one di
ation bounda
oundary of in
layout and b
s defined as
ent model, t
hours costs
the computa
model of Los
on at tidal st
ponding spec
bathymetry o
igital map f
ary of incom
ncoming wav
bathymetry o
20 m ( Δx) b
the time step
approx. 12 h
ational pow
s Angeles/Lo
tation as ma
ctral density
of LA/LB p
file is acquir
ming waves f
ves from we
of LA/LB po
by 20 m ( Δy
p Δt is 0.8 s
hours of com
er. White no
ong Beach P
arked by the
y distribution
port is used
red as Figur
from south,
est. Tidal stat
ort on extrem
y), and ther
s, and Coura
mputer work,
oise analysi
Port. Figure
star in Figu
n.
in the simu
re 6.31. The
and the grey
ation is mark
mely low tide
re are 382,50
ant number
, and Table 4
s would be
e 6.32~6.33
ure 6.31, and
14
ulation. Afte
e orange lin
y line denote
ked by star.
e
00 (750×510
is 0.684. Th
4.1 shows th
conducted i
illustrate th
d Figure 6.3
8
er
ne
es
0)
he
he
in
he
34
Fig
Figu
Fi
gure 6.32 Pre
ure 6.33 Pre
igure 6.34 S
edicted resp
edicted respo
Spectral dens
60.7 m
onse at tidal
onse at tidal
sity distribut
min
l station with
station with
tion of LA/L
h extremely
extremely l
LB port with
low tide (sou
low tide (we
extremely lo
14
uth source)
st source)
ow tide
9
Tidal
For t
spatia
mark
the ge
Figur
The r
cells
numb
and T
woul
6.36~
6.35,
l Level 2:
the present
al discretiza
ks the genera
eneration bo
re 6.35 The
resolution is
in the abov
ber is 0.684.
Table 4.1 sh
d be conduc
~6.37 illustra
and Figure
study, the b
ation, one di
ation bounda
oundary of in
layout and b
s defined as
ve model. In
. The simula
ows the con
cted in the
ate the nume
6.38 shows t
bathymetry o
igital map f
ary of incom
ncoming wav
bathymetry o
20 m ( Δx) b
n the presen
ation of 72 h
nfiguration o
numerical m
erical solutio
the correspo
of LA/LB p
file is acquir
ming waves f
ves from we
of LA/LB po
by 20 m ( Δy
nt model, the
hours costs
of the compu
model of Lo
on at tidal st
onding spectr
port is used
red as Figur
from south,
est. Tidal stat
ort on mean
y), and ther
e time step
approx. 12 h
utational pow
os Angeles/L
tation as mar
ral density d
in the simu
re 6.35. The
and the grey
ation is mark
low water
re are 382,50
Δt is 0.8 s,
hours of com
wer. White n
Long Beach
rked by the
distribution.
15
ulation. Afte
e orange lin
y line denote
ked by star.
00 (750×510
, and couran
mputer work
noise analys
h Port. Figur
star in Figur
0
er
ne
es
0)
nt
k,
is
re
re
F
F
F
Figure 6.36
igure 6.37 P
Figure 6.38
Predicted re
Predicted res
Spectral de
60
esponse at tid
sponse at tid
nsity distrib
0.7 min
35.3 m
dal station w
dal station wi
ution of LA/
min
26.8 min
with mean low
ith mean low
/LB port wit
18.5
min
w water (sou
w water (wes
th mean low
5
n
17.5
min
15
uth source)
st source)
w water
1
Tidal
For t
spatia
mark
the ge
Figur
The r
cells.
simul
confi
the n
nume
show
l Level 3:
the present
al discretiza
ks the genera
eneration bo
re 6.39 The
resolution is
In the pres
lation of 72
guration of
numerical m
erical solutio
ws the corresp
study, the b
ation, one di
ation bounda
oundary of in
layout and b
s defined as
sent model, t
hours costs
the computa
model of Los
on at tidal st
ponding spec
bathymetry o
igital map f
ary of incom
ncoming wav
bathymetry o
20 m ( Δx) b
the time step
approx. 12 h
ational pow
s Angeles/Lo
tation as ma
ctral density
of LA/LB p
file is acquir
ming waves f
ves from we
of LA/LB po
by 20 m ( Δy
p Δt is 0.8 s
hours of com
er. White no
ong Beach P
arked by the
y distribution
port is used
red as Figur
from south,
est. Tidal stat
ort on mean
y), and ther
s, and coura
mputer work,
oise analysi
Port. Figure
star in Figu
n.
in the simu
re 6.39. The
and the grey
ation is mark
tidal level
re are 382,50
ant number
, and Table 4
s would be
e 6.40~6.41
ure 6.39, and
15
ulation. Afte
e orange lin
y line denote
ked by star.
00 (750×510
is 0.684. Th
4.1 shows th
conducted i
illustrate th
d Figure 6.4
2
er
ne
es
0)
he
he
in
he
42
F
F
F
Figure 6.40
igure 6.41 P
Figure 6.42
Predicted re
Predicted res
Spectral den
60.7 m
5
esponse at tid
sponse at tid
nsity distribu
min
34.4
53.3 min
dal station w
dal station wi
ution of LA/L
min
26.5 min
with mean tid
ith mean tida
LB port with
n
dal level (sou
al level (wes
h mean tidal
15
uth source)
st source)
l level
3
Tidal
For t
spatia
mark
the ge
Figur
The r
cells.
simul
confi
the n
nume
show
l Level 4:
the present
al discretiza
ks the genera
eneration bo
re 6.43 The
resolution is
In the pres
lation of 72
guration of
numerical m
erical solutio
ws the corresp
study, the b
ation, one di
ation bounda
oundary of in
layout and b
s defined as
sent model, t
hours costs
the computa
model of Los
on at tidal st
ponding spec
bathymetry o
igital map f
ary of incom
ncoming wav
bathymetry o
20 m ( Δx) b
the time step
approx. 12 h
ational pow
s Angeles/Lo
tation as ma
ctral density
of LA/LB p
file is acquir
ming waves f
ves from we
of LA/LB po
by 20 m ( Δy
p Δt is 0.8 s
hours of com
er. White no
ong Beach P
arked by the
y distribution
port is used
red as Figur
from south,
est. Tidal stat
ort on mean
y), and ther
s, and coura
mputer work,
oise analysi
Port. Figure
star in Figu
n.
in the simu
re 6.43. The
and the grey
ation is mark
high water
re are 382,50
ant number
, and Table 4
s would be
e 6.44~6.45
ure 6.43, and
15
ulation. Afte
e orange lin
y line denote
ked by star.
00 (750×510
is 0.684. Th
4.1 shows th
conducted i
illustrate th
d Figure 6.4
4
er
ne
es
0)
he
he
in
he
46
F
F
Figure 6.44
igure 6.45 P
Figure 6.46
Predicted re
Predicted res
6 Spectral de
60.7 min
53
esponse at tid
sponse at tid
ensity distrib
n
3.3 min
31
dal station w
dal station wi
bution of LA
.4 min
25.2
min
m
with mean hig
ith mean hig
A/LB port wi
23.8
min
gh water (so
gh water (we
ith mean hig
15
outh source)
est source)
gh water
5
Tidal
For t
spatia
gener
gener
Figur
The r
cells
numb
and T
woul
6.48~
6.47,
l Level 5:
the present
al discretiza
ration bound
ration bound
re 6.47 The
resolution is
in the abov
ber is 0.684.
Table 4.1 sh
d be conduc
~6.49 illustra
and Figure
study, the b
ation, one di
dary of inc
dary of incom
layout and b
s defined as
ve model. In
. The simula
ows the con
cted in the
ate the nume
6.50 shows t
bathymetry o
gital map fi
coming wav
ming waves
bathymetry o
20 m ( Δx) b
n the presen
ation of 72 h
nfiguration o
numerical m
erical solutio
the correspo
of LA/LB p
ile is as Figu
ves from sou
from west. T
of LA/LB po
by 20 m ( Δy
nt model, the
hours costs
of the compu
model of Lo
on at tidal st
onding spectr
port is used
ure 6.47. Th
uth, and th
Tidal station
ort on extrem
y), and ther
e time step
approx. 12 h
utational pow
os Angeles/L
tation as mar
ral density d
in the simu
he orange li
he grey line
n is marked b
mely high tid
re are 382,50
Δt is 0.8 s,
hours of com
wer. White n
Long Beach
rked by the
distribution.
15
ulation. Afte
ine marks th
e denotes th
by star.
de
00 (750×510
, and couran
mputer work
noise analys
h Port. Figur
star in Figur
6
er
he
he
0)
nt
k,
is
re
re
Fig
Fig
Fig
gure 6.48 Pr
gure 6.49 Pr
gure 6.50 Sp
redicted resp
redicted resp
pectral densi
69.2
min
60.7 m
ponse at tida
ponse at tida
ity distributi
min
36.2 m
al station with
al station with
ion of LA/LB
min
26.8 min
h extremely
h extremely
B port with e
high tide (s
high tide (w
extremely hi
15
outh source)
west source)
igh tide
7
)
Integ
oscill
sensit
Figur
The t
and t
with
oscill
and b
grate the wa
lation R by t
tivity on a
re 6.51 is acq
Figure 6.5
tidal levels in
he harbor is
incident wav
lation than t
blocking the
ave spectrum
the incident
given tidal
quired as fol
1 The sensi
n the above
s equally sen
ves from sou
he ones of w
west.
m by freque
wave energy
level. Repe
llow.
itivity of LA
curves are in
nsitive on mo
uth. The inc
west source,
ency and div
y I. The ratio
eat the same
A/LB port on
ndicated by
ost the tidal
ident waves
because the
vide the res
o R/I can be
e process fo
n various tida
the water de
levels excep
s coming fro
e breakwater
sulting ener
e used to rep
or all the tid
al levels
epth at tidal
pt the extrem
om south ind
r is opening
15
rgy of harbo
present harbo
de levels, th
gauge statio
mely low tid
duces stronge
g to the south
8
or
or
he
on,
de
er
h,
6
As th
differ
Table
Tida
For e
ideali
same
F
6.3.3 San D
he first step
rent tidal lev
e 6.4 Chosen
al Level
1
2
3
4
5
each of the
ized inciden
for all the f
igure 6.52 T
iego Harbo
p, it is intere
vels as shown
n tidal levels
W
ex
mean lo
mean ti
mean hi
ext
tidal levels
nt wave train
five tidal leve
The incident
r
esting to inv
n in Table 6
s of San Die
Water Levels
xtremely low
ow water (M
idal level (M
igh water (M
tremely high
above, a n
n as in Figur
els, their am
t wave for w
vestigate the
.4.
ego harbor
w
MLW)
MTL)
MHW)
h
numerical m
re 6.52. Wh
mplitudes are
white noise an
e behavior
D
model is buil
hile the shap
scaled to eq
nalysis in Sa
of San Dieg
Depth at Sta
1.0 m
1.5 m
2.0 m
2.6 m
3.0 m
lt and simul
e of inciden
qualize nonli
an Diego har
15
go harbor o
ation
lated with a
nt wave is th
inearity.
rbor
9
on
an
he
Tidal
For th
spatia
mark
the ge
Figur
The r
The t
2 hou
powe
star in
l Level 1:
he present st
al discretiza
ks the genera
eneration bo
re 6.53 The
resolution ha
time step Δt
urs of comp
er. Figure 6.
n Figure 6.5
tudy, the bat
ation, one di
ation bounda
oundary of in
layout and b
as been defin
is 1.2 s, and
uter work, a
54~6.55 sho
3, and Figur
thymetry of
igital map f
ary of incom
ncoming wav
bathymetry o
ned as 40 m
d Courant nu
and Table 4
ow the num
re 6.56 show
San Diego h
file is acquir
ming waves f
ves from we
of San Diego
m ( Δx) by 40
umber is 0.6
.1 shows the
merical soluti
ws the corresp
harbor is use
red as Figur
from south,
est. Tidal stat
o harbor on e
0 m ( Δy), and
631. The sim
e configurat
ion at tidal
ponding spe
ed in the sim
re 6.53. The
and the grey
ation is mark
extremely lo
d there are 1
mulation of 4
tion of the c
station as m
ectral density
16
mulation. Afte
e orange lin
y line denote
ked by star.
ow tide
159,600 cell
48 hours cost
computationa
marked by th
y distribution
0
er
ne
es
s.
ts
al
he
n.
Fig
Fig
Fig
gure 6.54 Pr
gure 6.55 Pr
gure 6.56 Sp
redicted resp
redicted resp
pectral densit
273 min
6
ponse at tida
ponse at tida
ty distributio
66.1 min
30.1
33.6
min
al station with
al station with
on of San Di
min
26.9 min
21.8 min
h extremely
h extremely
iego harbor w
17.8 min
13.9
low tide (so
low tide (w
with extrem
9 min
16
outh source)
west source)
ely low tide
1
Tidal
For th
spatia
mark
the ge
Figur
The r
The t
2 hou
powe
star in
l Level 2:
he present st
al discretiza
ks the genera
eneration bo
re 6.57 The
resolution ha
time step Δt
urs of comp
er. Figure 6.5
n Figure 6.5
tudy, the bat
ation, one di
ation bounda
oundary of in
layout and b
as been defin
is 1.2 s, and
uter work, a
58~6.59 illu
7, and Figur
thymetry of
igital map f
ary of incom
ncoming wav
bathymetry o
ned as 40 m
d Courant nu
and Table 4
strate the nu
re 6.60 show
San Diego h
file is acquir
ming waves f
ves from we
of San Diego
m ( Δx) by 40
umber is 0.6
.1 shows the
umerical solu
ws the corresp
harbor is use
red as Figur
from south,
est. Tidal stat
o harbor on m
0 m ( Δy), and
631. The sim
e configurat
ution at tidal
ponding spe
ed in the sim
re 6.57. The
and the grey
ation is mark
mean low w
d there are 1
mulation of 4
tion of the c
l station as m
ectral density
16
mulation. Afte
e orange lin
y line denote
ked by star.
water
159,600 cell
48 hours cost
computationa
marked by th
y distribution
2
er
ne
es
s.
ts
al
he
n.
F
F
Fig
Figure 6.58
igure 6.59 P
gure 6.60 Sp
Predicted re
Predicted res
pectral densit
273 min
78
m
esponse at tid
sponse at tid
ty distributio
30
mi
8
min
60.7
min
dal station w
dal station wi
on of San Di
0.3
in
26.9 min
1
25.6
min
with mean low
ith mean low
iego harbor w
17.8 min
14.4 m
w water (sou
w water (wes
with mean lo
min
16
uth source)
st source)
ow water
3
Tidal
For th
spatia
mark
the ge
Figur
The r
The t
2 hou
powe
star in
l Level 3:
he present st
al discretiza
ks the genera
eneration bo
re 6.61 The
resolution ha
time step Δt
urs of comp
er. Figure 6.6
n Figure 6.6
tudy, the bat
ation, one di
ation bounda
oundary of in
layout and b
as been defin
is 1.2 s, and
uter work, a
62~6.63 illu
1, and Figur
thymetry of
igital map f
ary of incom
ncoming wav
bathymetry o
ned as 40 m
d Courant nu
and Table 4
strate the nu
re 6.64 show
San Diego h
file is acquir
ming waves f
ves from we
of San Diego
m ( Δx) by 40
umber is 0.6
.1 shows the
umerical solu
ws the corresp
harbor is use
red as Figur
from south,
est. Tidal stat
o harbor on m
0 m ( Δy), and
631. The sim
e configurat
ution at tidal
ponding spe
ed in the sim
re 6.61. The
and the grey
ation is mark
mean tidal le
d there are 1
mulation of 4
tion of the c
l station as m
ectral density
16
mulation. Afte
e orange lin
y line denote
ked by star.
evel
159,600 cell
48 hours cost
computationa
marked by th
y distribution
4
er
ne
es
s.
ts
al
he
n.
F
F
Fig
Figure 6.62
igure 6.63 P
gure 6.64 Sp
Predicted re
Predicted res
pectral densi
273 min
81
mi
esponse at tid
sponse at tid
ity distributi
.9
in
58.5
min
30
mi
dal station w
dal station wi
ion of San D
26.8 min
25.6
min
0.0
in
23.8
min
21.6
with mean tid
ith mean tida
Diego harbor
min
13.9
min
dal level (sou
al level (wes
with mean t
13.2
min
16
uth source)
st source)
tidal level
5
Tidal
For th
spatia
mark
the ge
Figur
The r
The t
2 hou
powe
star in
l Level 4:
he present st
al discretiza
ks the genera
eneration bo
re 6.65 The
resolution ha
time step Δt
urs of comp
er. Figure 6.6
n Figure 6.6
tudy, the bat
ation, one di
ation bounda
oundary of in
layout and b
as been defin
is 1.2 s, and
uter work, a
66~6.67 illu
5, and Figur
thymetry of
igital map f
ary of incom
ncoming wav
bathymetry o
ned as 40 m
d Courant nu
and Table 4
strate the nu
re 6.68 show
San Diego h
file is acquir
ming waves f
ves from we
of San Diego
m ( Δx) by 40
umber is 0.6
.1 shows the
umerical solu
ws the corresp
harbor is use
red as Figur
from south,
est. Tidal stat
o harbor on m
0 m ( Δy), and
631. The sim
e configurat
ution at tidal
ponding spe
ed in the sim
re 6.65. The
and the grey
ation is mark
mean high w
d there are 1
mulation of 4
tion of the c
l station as m
ectral density
16
mulation. Afte
e orange lin
y line denote
ked by star.
water
159,600 cell
48 hours cost
computationa
marked by th
y distribution
6
er
ne
es
s.
ts
al
he
n.
F
F
Fi
Figure 6.66
igure 6.67 P
igure 6.68 S
Predicted re
Predicted res
Spectral dens
273 min
esponse at tid
sponse at tid
sity distribut
78 min
54.6 min
2
m
dal station w
dal station wi
tion of San D
25.6 min
23.7 min
26.8
min
21.6
min
with mean hig
ith mean hig
Diego harbor
18.1 min
13
gh water (so
gh water (we
r with mean
3.2 min
16
outh source)
est source)
high water
7
Tidal
For th
spatia
mark
the ge
Figur
The r
The t
2 hou
powe
star in
l Level 5:
he present st
al discretiza
ks the genera
eneration bo
re 6.69 The
resolution ha
time step Δt
urs of comp
er. Figure 6.7
n Figure 6.6
tudy, the bat
ation, one di
ation bounda
oundary of in
layout and b
as been defin
is 1.2 s, and
uter work, a
70~6.71 illu
9, and Figur
thymetry of
igital map f
ary of incom
ncoming wav
bathymetry o
ned as 40 m
d Courant nu
and Table 4
strate the nu
re 6.72 show
San Diego h
file is acquir
ming waves f
ves from we
of San Diego
m ( Δx) by 40
umber is 0.6
.1 shows the
umerical solu
ws the corresp
harbor is use
red as Figur
from south,
est. Tidal stat
o harbor on e
0 m ( Δy), and
631. The sim
e configurat
ution at tidal
ponding spe
ed in the sim
re 6.69. The
and the grey
ation is mark
extremely hi
d there are 1
mulation of 4
tion of the c
l station as m
ectral density
16
mulation. Afte
e orange lin
y line denote
ked by star.
igh tide
159,600 cell
48 hours cost
computationa
marked by th
y distribution
8
er
ne
es
s.
ts
al
he
n.
F
F
Fig
Figure 6.70
igure 6.71 P
gure 6.72 Sp
Predicted re
Predicted res
pectral densit
273 min
86
mi
esponse at tid
sponse at tid
ty distributio
60.7 min
.2
in
dal station w
dal station wi
on of San Di
25.6 min
23.7 min
21.6
min
26.8
min
with extremel
ith extremely
iego harbor w
17.8 min
13
ly high tide
y high tide (
with extrem
3.2 min
16
(south sourc
(west source
ely high tide
9
ce)
e)
e
Integ
oscill
harbo
the F
The t
and th
to be
west
speci
the s
bendi
grate the wa
lation R by
or sensitivity
igure 6.73 is
Figure 6.7
tidal levels in
he harbor is
slightly mo
induce sligh
ial layout an
outh, the ha
ing, in certai
ave spectrum
the incident
y on a given
s acquired as
73 The sensi
n the above
similarly se
ore sensitive
htly stronge
d orientation
arbor has ho
in extent, eli
m by freque
t wave energ
n tidal level.
s follow.
itivity of San
curves are in
ensitive on m
than the hig
er oscillation
n of San Die
ook-like sha
iminates the
ency and div
gy I. The ra
Repeat the
n Diego harb
ndicated by
most the tidal
gher tidal lev
n than the o
ego harbor. E
ape which tu
impact of di
vide the res
atio R/I can
same proce
bor on variou
the water de
l levels. The
vel. The inci
ones of south
Even though
urns around
irection of in
sulting ener
be used to
ess for all th
us tidal level
epth at tidal
e lower tidal
ident waves
h source, be
h the entranc
by approx.
ncoming wa
17
rgy of harbo
represent th
he tide level
ls
gauge statio
level appear
coming from
ecause of th
ce is facing t
147 . Th
ave.
0
or
he
s,
on,
rs
m
he
to
is
6.4 W
6
After
entire
a ran
gridd
6.2. T
Mar.
levels
Ocea
south
tide.
“sout
Figur
White Noise
6.4.1 Cresce
r analysis on
e tidal period
nge given b
ding system,
The Figure 6
1
st
, 2010 an
s. The tidal
anic and Atm
h source and
Therefore, t
th high”, “we
re 6.74 Tide
e Analysis o
ent City Ha
n each singl
ds. Through
y tidal gaug
tidal fluctua
6.74 and Fig
nd from Ma
data is acq
mospheric Ad
d west sourc
there are fou
est low”, and
e of Crescent
n Fluctuatin
arbor
le tidal leve
out the mod
ge records
ation is discr
gure 6.75 sh
r. 11
th
, 2011
quired from
dministration
e are loaded
ur scenarios
d “west high
t City harbor
low sta
ng Tidal Le
l, it is inter
deling proces
from NOAA
retized into t
how the tida
1 to Mar. 13
local tidal
n (NOAA).
d into the nu
all together,
h”.
r based on w
art
evel
resting to sim
ss, the tidal l
A. Due to t
the five repr
al fluctuation
3
th
, 2011, wi
gauge statio
In this secti
umerical sys
, and they ar
water depth a
mulate oscil
level is set t
the limitatio
resentative le
n from Feb.
ith the five
on operated
on, the incid
stem at low
re named as
at station (so
high start
17
llation withi
to fluctuate i
on of presen
evels in Tabl
27
th
, 2010 t
chosen wate
d by Nationa
dent waves o
tide and hig
“south low”
outh source)
1
in
in
nt
le
to
er
al
of
gh
”,
Figur
Use t
given
south
tidal
from
Figu
re 6.75 Tide
the incident w
n time. Figu
h source wav
level, west s
high tidal le
ure 6.76 Pred
e of Crescent
wave illustra
ure 6.76~6.7
ve starting f
source wave
evel.
dicted respon
low s
t City harbor
ated in Figur
79 show the
from low tid
e starting fro
nse at tidal s
start
r based on w
re 6.7, and s
e numerical
dal level, so
om low tidal
station startin
water depth a
switch the m
solutions a
outh source
level, and w
ng with low
high start
at station (we
model with tid
at tidal statio
wave startin
west source
tide (south
17
est source)
dal levels in
on, includin
ng from hig
wave startin
source)
2
a
ng
gh
ng
F
F
F
igure 6.77 P
igure 6.78 P
igure 6.79 P
Predicted res
Predicted res
Predicted res
sponse at tid
sponse at tid
sponse at tid
dal station sta
dal station sta
dal station sta
arting with h
arting with l
arting with h
high tide (sou
low tide (we
high tide (we
17
uth source)
st source)
est source)
3
Take
spectra for t
Figure 6.
Figure 6
the solutions
80 Spectral
6.81 Spectra
s of Fig 6.76
density of s
al density of
24.8 m
2
26.6
min
28.8
min
24.8
26.6 min
25.7 min
6~Fig 6.79, a
south source
west source
21.6 min min
19.2 m
3.2 min
min
21.5
min
22.5 min
19.7
min
1
and compare
scenarios in
scenarios in
min
18.2 min
15.2
17.6 min
7
n
19.0 min
18.2 min
16.5 min
e as Fig 6.80
n Crescent C
n Crescent C
2 min
n
17
0~Fig 6.81.
City harbor
City harbor
4
Fig 6
ascer
norm
respo
Figur
Figur
6.80 and Fig
rtained by r
malizing with
onse and gau
re 6.82 Spec
re 6.83 Spec
6.81 show t
realistic resp
h the maxim
uge reading o
tra of white
tra of white
the spectra o
ponse at ti
mum wave s
of historical
noise analys
noise analys
of idealized i
dal station
spectrum va
tsunamis are
sis and histo
sis and histo
incoming wa
in Crescen
alue (S
max
),
e compared
orical tsunam
orical tsunam
aves, and th
nt City harb
the spectra
as Fig 6.82 a
mi in Crescen
mi in Crescen
17
hey need to b
bor. Throug
of predicte
and Fig 6.83
nt City harbo
nt City harbo
5
be
gh
ed
3.
or
or
The F
of ha
multi
water
with
F
Fig 6.82 and
arbor layout
iple resonant
r level recor
tsunami eve
Figure 6.84
filtered ou
filtered ou
(a)
(b)
d Fig 6.83 sh
lead to the
t modes are
rd on norma
nt on Mar. 1
(a) The spe
ut at Crescen
(b) The spe
ut at Crescen
51.2
72.5 min
how that fluc
multiple re
also observ
al day with
11
th
, 2011 as
ectral density
nt City harbo
ctral density
nt City harbo
25.8
30.3 min
2 min
n
ctuating tida
esonant mod
ved on norma
fast Fourier
Figure 6.84
y distribution
or on normal
y distribution
or on tsunam
min
21.8 min
17.8
al level and t
des in histor
al days. Lee
r transformat
4.
n of tide gau
day (07/21/
n of tide gau
mi event (03/1
min
17.0 min
the correspo
rical tsunam
e, et. al (201
tion (FFT),
uge records w
/2008)
uge records w
11/2011)
17
nding chang
i events. Th
3) treated th
and compar
with tide
with tide
6
ge
he
he
re
Figur
if the
long
Lee e
Figur
2008
prima
stand
17.5
as the
multi
re 6.84 show
ere are no tsu
time (in day
et. al (2013)
Figure 6.85
re 6.85 analy
in Crescent
ary resonant
ds for the ene
minutes and
e correspond
iple resonant
ws that the m
unami event
ys), this phe
also conduc
Wave spec
yzes the spe
t City harbo
t mode. Th
ergy of tides
d 83.3 minut
ding change
t modes.
multiple reso
ts. As long a
enomenon w
cted spectral
ctrum of May
ctral density
r, and this o
e high ener
s, meanwhile
es. This dem
caused to th
nant modes
as the effect
will occur in
analysis for
y, June, July
y distribution
overall spect
rgy compon
e, multiple r
monstrates th
he layout of h
are happeni
of tidal fluc
Crescent Ci
r a three mon
y of 2008 at
n of waves i
trum demon
nent at botto
esonant mod
hat the fluctu
harbor are th
ing on norm
ctuation keep
ity harbor. T
nth record, a
Crescent Cit
in May, June
nstrates 22 m
om part of
des are obse
uating tidal l
he reasons th
17
mal days, eve
ps for enoug
To prove thi
as Figure 6.8
ty Harbor
e, and July o
minutes as th
the spectrum
rved betwee
levels as we
hat lead to th
7
en
gh
s,
85.
of
he
m
en
ell
he
The p
harbo
espec
and c
Dece
was b
and 3
1
st
of
conta
min a
(a
(c
present pape
our to fortif
cially the spi
correspondin
mber 1
st
in
between 1.0
3.6 m; On Ju
f 2013, wat
ains multiple
and 25 min.
)
)
er investigate
fy the argum
ikes between
ng spectral
2013 are de
m and 3.2 m
une 1
st
of 201
ter depth wa
e spikes, and
es four repre
ment that ti
n 20 min an
density dist
emonstrated
m; On Decem
13, water dep
as between
d stronger tid
esentative n
ide fluctuat
nd 25 min. T
tribution on
as Figure 9
mber 1
st
of 2
pth was betw
1.3 m and
de fluctuation
normal days
tion influenc
The water de
March 1
st
,
. On March
2013, water d
ween 1.2 m a
3.1 m. The
n generates b
(b)
(d)
in 2013 in C
ces the reso
epth at tide
June 1
st
, S
h 1
st
of 2013
depth was b
and 3.0 m; O
e normal da
bigger spike
17
Crescent Cit
onant mode
gauge statio
eptember 1
s
, water dept
etween 0.5 m
On Septembe
ay oscillatio
es between 2
8
ty
s,
on
st
,
th
m
er
on
20
(e
(g
Fig
on M
2013
1
st
, 20
Figur
norm
will c
mode
chang
min a
spike
)
g)
gure 6.86. W
March 1
st
, 201
(Source: N
013; (d) on J
re 9 indicate
mal days, wh
change the h
es as variabl
ge of harbou
and 25 min
es, especially
Water depth
13; (c) on Ju
OAA); The
June 1
st
, 201
es that mult
ich results o
harbour layo
e spikes in t
ur layout is
. Therefore,
y between 20
h at tide gaug
une 1
st
, 2013
spectral den
3; (f) on Sep
tiple spikes
of energy co
out and bathy
the spectrum
explicitly a
the tide of
0 min and 25
ge (Station D
; (e) on Sept
nsity distribu
ptember 1
st
,
exist, not o
ontent of inc
ymetry, and
m. The fluctu
associated w
f larger amp
5 min in Cre
(f)
(h)
Datum) in C
tember 1
st
, 2
ution with ti
2013; (h) on
only on tsun
coming long
will ultimat
uation of tide
with the reso
plitude will
scent City h
Crescent Cit
2013; (g) on
ide filtered
n December
nami events
waves. The
tely indicate
e level and c
onant periods
generate big
harbour.
17
ty harbour (a
December 1
(b) on Marc
1
st
, 2013
, but also o
e moving tid
e the resonan
correspondin
s between 2
gger multipl
9
a)
1
st
,
ch
on
de
nt
ng
20
le
The s
tide h
m an
these
spect
Figur
1
st
to
from
Figur
norm
spring tide fr
height is 3.0
d 2.5 m, and
two time se
tral density d
re 6.87 (a). S
Jan. 5
th
, 20
April. 6
st
to
re 6.87 provi
mal days, and
(a)
(b)
rom Jan. 1
st
t
m. The nea
d the tide he
essions, and
distribution c
Spectral dens
014; (b). Spe
Jan. 10
th
, 20
ides a firm e
d the larger ti
to Jan. 5
th
, 2
ap tide from
eight is 1.0 m
the wave el
curves as sho
sity distribut
ectral densit
014;
evidence tha
ide fluctuatio
2014 fluctuat
Apr. 6
th
to A
m. There wa
levation at t
own in Figur
tion with tid
y distributio
at the multip
on is correla
ted between
Apr. 9
th
, 201
as no tsunam
tide gauge st
re 6.87.
de filtered du
on with tide
le spectral s
ated with hig
0.5 m and 3
14 fluctuated
mi event hap
tation is tran
uring spring
filtered dur
spikes comm
gher energy.
18
3.5 m, and th
d between 1.
ppened durin
nsformed int
tide from Ja
ring neap tid
monly exist o
0
he
.5
ng
to
an.
de
on
6
After
entire
a ran
gridd
Table
2010
water
Natio
wave
and h
as “so
6.4.2 Los A
r analysis on
e tidal period
nge given b
ding system,
e 6.3. The F
to Mar. 1
st
,
r levels. Th
onal Oceanic
es of south s
high tide. Th
outh low”, “
Figure 6.88
ngeles/Long
n each singl
ds. Through
y tidal gaug
tidal fluctua
Figure 6.88
2010 and fr
he tidal data
c and Atmos
source and w
herefore, the
south high”,
Tide of LA
g Beach Por
le tidal leve
out the mod
ge records
ation will be
and Figure
rom Mar. 11
a is acquire
spheric Adm
west source a
ere would be
, “west low”
A/LB port ba
low start
rt
l, it is inter
deling proces
from NOAA
e discretized
6.89 show
1
th
, 2011 to M
ed from loc
ministration (
are loaded in
e four scenar
”, and “west
ased on wate
resting to sim
ss, the tidal l
A. Due to t
d into the fiv
the tidal flu
Mar. 13
th
, 20
cal tidal ga
(NOAA). In
nto the num
rios all toge
high”.
er depth at st
hig
mulate oscil
level is set t
the limitatio
ve representa
uctuation fro
011, with th
auge station
this section
merical system
ether, and the
tation (south
gh start
18
llation withi
to fluctuate i
on of presen
ative levels i
om Feb. 27
t
he five chose
operated b
n, the inciden
m at low tid
ey are name
h source)
1
in
in
nt
in
th
,
en
by
nt
de
ed
Use t
a giv
wave
sourc
level
Figu
Figure 6.89
the incident
ven time. Fi
e starting fro
ce wave star
.
ure 6.90 Pre
9 Tide of LA
wave illustra
igure 6.90~6
om low tidal
ting from lo
edicted respo
low start
A/LB port ba
ated in Figu
6.93 show t
level, south
ow tidal leve
onse at tidal
ased on wate
ure 6.30, and
the numeric
h source wav
el, and west
station starti
hig
er depth at st
d switch the m
al solutions
ve starting fr
source wave
ing with low
gh start
tation (west
model with t
, including
rom high tid
e starting fro
w tide (south
18
source)
tidal levels i
south sourc
dal level, we
om high tida
source)
2
in
ce
st
al
Figu
Figu
Figu
ure 6.91 Pred
ure 6.92 Pre
ure 6.93 Pre
dicted respon
edicted respo
edicted respo
nse at tidal s
onse at tidal
onse at tidal
station startin
station starti
station starti
ng with high
ing with low
ing with hig
h tide (south
w tide (west s
gh tide (west
18
h source)
source)
source)
3
Take
spectra for t
Figure
Figu
the solutions
e 6.94 Spect
ure 6.95 Spe
75.8
min
58.5 min
55.4 min
51.2 mi
75.8
min
58.5 min
53.9 min
s of Fig 6.90
tral density o
ectral density
n
n
in
26.9 m
n
35.3 min
0~Fig 6.93, a
of south sou
y of west sou
min
and compare
urce scenario
urce scenario
e as Fig 6.94
os in LA/LB
os in LA/LB
18
4 and Fig 6.9
port
B port
4
95.
From
stron
Secti
spect
tide.
startin
level
neces
the hi
Throu
gauge
Fi
m Fig 6.96 an
ger oscillati
on 6.3. For s
tral density d
For west so
ng point cha
and varying
ssary to com
istorical tsun
ugh normali
e reading of
igure 6.96 S
nd Fig 6.97,
on than the
south source
drops by 34
urce oscillat
anges from
g harbor layo
mpare the num
nami oscillat
zing by the
f historical ts
Spectra of wh
it can be se
ones from
e oscillations
.4%, when t
tions, the fu
high tide to
out has been
merical solut
tion.
maximum p
unami event
hite noise an
een that wav
west, which
s, the fundam
the starting
ndamental f
o low tide. S
n analyzed by
tions with da
peak values,
ts can be com
nalysis and h
ves coming f
h agrees wit
mental frequ
point chang
frequency do
So far, the e
y numerical
ata observed
the spectra o
mpared as F
historical tsun
from south s
th the earlier
uency keeps t
ges from hig
oes not chan
effect of flu
l simulation,
d by tidal ga
of numerical
ig 6.96 and F
unami in LA/
18
source induc
r solutions i
the same, an
gh tide to low
nge, when th
uctuating tida
and it is als
auge station i
l solution an
Fig 6.97.
/LB Port
5
ce
in
nd
w
he
al
so
in
nd
Fig
Due t
throu
obser
gure 6.97 Sp
to the topog
ugh the entir
rved.
pectra of wh
graphy of Lo
re tidal peri
hite noise ana
os Angeles/L
od, and no
alysis and hi
Long Beach
significant c
istorical tsun
h Port, the ha
change of f
nami in LA/L
arbor layout
fundamental
18
LB Port
t keeps stabl
frequency
6
le
is
6
After
entire
a ran
gridd
6.4. T
Mar.
levels
Ocea
south
tide.
“sout
F
6.4.3 San D
r analysis on
e tidal period
nge given b
ding system,
The Figure 6
1
st
, 2010 an
s. The tidal
anic and Atm
h source and
Therefore, t
th high”, “we
igure 6.98 T
iego Harbo
n each singl
ds. Through
y tidal gaug
tidal fluctua
6.98 and Fig
nd from Ma
data is acq
mospheric Ad
d west sourc
there are fou
est low”, and
Tide of San D
r
le tidal leve
out the mod
ge records
ation is discr
gure 6.99 sh
r. 11
th
, 2011
quired from
dministration
e are loaded
ur scenarios
d “west high
Diego harbo
low start
l, it is inter
deling proces
from NOAA
retized into t
how the tida
1 to Mar. 13
local tidal
n (NOAA).
d into the nu
all together,
h”.
or based on w
high start
resting to sim
ss, the tidal l
A. Due to t
the five repr
al fluctuation
3
th
, 2011, wi
gauge statio
In this secti
umerical sys
, and they ar
water depth a
mulate oscil
level is set t
the limitatio
resentative le
n from Feb.
ith the five
on operated
on, the incid
stem at low
re named as
at station (so
18
llation withi
to fluctuate i
on of presen
evels in Tabl
27
th
, 2010 t
chosen wate
d by Nationa
dent waves o
tide and hig
“south low”
outh source)
7
in
in
nt
le
to
er
al
of
gh
”,
F
Use t
a giv
wave
sourc
level
Figu
igure 6.99 T
the incident
ven time. Fig
e starting fro
ce wave star
.
ure 6.100 Pre
Tide of San D
wave illustra
gure 6.100~6
om low tidal
ting from lo
edicted resp
low start
Diego harbor
ated in Figu
6.103 show
level, south
ow tidal leve
onse at tidal
r based on w
ure 6.52, and
the numeric
h source wav
el, and west
l station start
hig
water depth a
d switch the m
cal solutions
ve starting fr
source wave
ting with low
gh start
at station (we
model with t
s, including
rom high tid
e starting fro
w tide (south
18
est source)
tidal levels i
south sourc
dal level, we
om high tida
h source)
8
in
ce
st
al
Figu
Figu
Figu
ure 6.101 Pre
ure 6.102 Pre
ure 6.103 Pre
edicted resp
edicted resp
edicted resp
onse at tidal
onse at tidal
onse at tidal
l station start
l station start
l station start
ting with hig
ting with low
ting with hig
gh tide (sout
w tide (west
gh tide (west
18
th source)
source)
t source)
9
Take
spectra for F
Figure 6
Figure 6.1
Fig 6.100~F
6.104 Spectr
105 Spectra
81.9 min
273 min
81.9
min
273
mi n
Fig 6.103, an
ral density of
al density of
53.9 min
53.9 min
26.9
45.5
min
34.7
min
nd compare a
f south sourc
west source
26.9 min
29.7
min
21.3
9 min
29.7
min
21.3
25.3 min
23.8 min
23.0 mi
as Fig 6.104
ce scenarios
scenarios in
3 min
3 min
n
in
17.8 min
and Fig 6.10
in San Dieg
n San Diego
14.9 min
14.9 min
15.0 min
13.4 min
19
05.
go harbor
harbor
0
From
inten
Secti
minu
west
minu
fluctu
by nu
data o
Throu
gauge
Figu
m Fig 6.104
sive oscillat
on 6.3. For
utes to 25.3 m
source oscil
utes, when th
uating tidal
umerical sim
observed by
ugh normali
e reading can
ure 6.106 Sp
and Fig 6
tion than the
south source
minutes, wh
llations, the
he starting po
level and th
mulation, and
tidal gauge
zing by the
n be compar
pectra of wh
6.105, wave
e ones from
e oscillations
en the startin
fundamenta
oint changes
he correspon
d it is also ne
station in th
maximum p
red as Fig 6.
hite noise ana
es coming f
west, which
s, the fundam
ng point cha
al frequency
s from high
ding change
ecessary to c
he historical t
peak values,
106 and Fig
alysis and hi
from south
h agrees wit
mental frequ
anges from h
y switches fr
tide to low
e of harbor l
compare the
tsunami osc
the spectra o
g 6.107.
istorical tsun
source indu
th the earlie
uency switch
high tide to
rom 25.3 mi
tide. So far,
layout has b
numerical s
illation.
of numerical
nami in San
19
uce similarl
r solutions i
hes from 81.
low tide. Fo
inutes to 26.
, the effect o
been analyze
solutions wit
l solution an
Diego harbo
1
ly
in
.9
or
.9
of
ed
th
nd
or
Figu
Fig 6
corre
ure 6.107 Sp
6.106 and F
sponding ch
pectra of wh
Fig 6.107 d
hange of harb
hite noise ana
demonstrate
bor layout in
alysis and hi
the effect
n the oscillat
istorical tsun
of fluctuat
tion induced
nami in San
ting tidal le
d by strong ts
19
Diego harbo
evel and th
sunamis.
2
or
he
193
6.5 Summary
This chapter studies oscillation of Crescent City harbor, Los Angeles/Long Beach Port,
and San Diego harbor, based on different tidal levels. Due to the topography of seabed, a
changed tidal level might induce different bathymetry and harbor layout. If so, there will
be multiple resonant modes or the primary resonant mode will be different, as can be seen
in cases of Crescent City harbor and San Diego harbor. If the harbor layout does not
change with tidal level, the harbor will retain the same resonant mode, such as Los
Angeles/Long Beach Port. For Crescent City harbor, different tidal levels can affect its
response intensity to long waves, and the most sensitive condition is when water depth at
station is about 1.2 m. For Los Angeles/Long Beach Port and San Diego harbor, the
response will keep relatively stable along changing tidal levels, with sensitivity slightly
higher at lower tidal level.
In addition, fluctuating tidal level is also taken into account to investigate the multiple
resonant modes and shift of primary resonant mode in historical cases. It was observed
that continuously changing tidal level is an important factor that caused the multiple
resonant modes, and the corresponding change of harbor layout can change the resonant
mode of harbor.
In this chapter, study is focused on idealized incident waves. In the next chapter, practical
incident wave profiles are introduced to further disclose the reasons that contribute to the
oscillation events on Feb. 27
th
, 2010 and Mar. 11
th
, 2011.
194
CHAPTER 7: INVESTIGATION OF HISTORICAL OSCILLATION CASES
In this chapter, the incoming waves of Feb. 27
th
, 2010 Chilean earthquake-tsunami and
Mar. 11
th
, 2011 Tohoku Earthquake-tsunami are introduced to find out the reasons that
caused the unusual resonant response in Crescent City and San Diego harbor. The input
data is described in Section 7.1, and simulation results is discussed in Section 7.2 and 7.3.
7.1 Source of Data
There are three types of data in this section, including the observed data from local the
tidal station, predicted response by present model with realistic incoming waves, and
predicted response by MOST inundation model.
Table 7.1 Three Types of Data of Concern
Type Source of Input Simulation Model Usage of Output
1
Wave surface elevation recorded by
tide gauge
N/A reference
2
Incident wave train provided by
MOST propagation model used as
the incident wave for present
numerical model
present numerical
model
to compare with
reference
3
Predicted water surface elevation at
tide gauge station
MOST
to compare with
reference
The concerned factors are the fluctuating tidal level as well as the corresponding change
of harbor layout. In reality, the records of incident waves are very scarce, because the
ocean has such an enormous area that people cannot record the tsunami waves at any
given location. Therefore, it is necessary to choose a wave train that represents the truth
as much as possible and the propagation model of MOST is used to provide realistic
incoming waves that are calibrated with records of deep ocean buoys.
7.2 T
7
The t
impa
Figu
The
calibr
Fig
Tsunami Ca
7.2.1 Cresce
tidal gauge i
ct time of Ch
ure 7.1 Tidal
data of inci
rated by buo
gure 7.2 Inc
aused by Ch
ent City Har
in Crescent
hilean earthq
l gauge reco
ident waves
oy records in
cident waves
hile Earthqu
rbor
City harbor
quake-tsunam
rds on 02/27
is acquire
n deep ocean
s for Crescen
uake on Feb
r records wa
mi on Feb. 2
7/2010 in Cr
ed from pro
n. The incide
nt City harbo
b. 27
th
, 2010
ater level (St
27
th
, 2010, as
rescent City
opagation m
ent waves are
or (source: S
0
tation Datum
s shown in F
Harbor (sou
model of MO
e shown in F
Sangyoung S
19
m) during th
Figure 7.1.
urce: NOAA)
OST, and ar
Figure 7.2.
Son)
5
he
)
re
Simu
respo
F
Trans
frequ
ulate oscillat
onse with tid
Figure 7.3
Figure 7.4 P
sform the re
uencies betw
tion with in
dal gauge rec
Predicted re
Predicted res
esponses int
een 3×10
-4
h
ncoming wa
cords and pre
esponse, solu
sponse, solut
to spectra as
hz and 10×10
aves in Figu
ediction by M
ution by MO
tion by MOS
s shown in
0
-4
hz are inv
ure 7.2, and
MOST in Fig
OST and gaug
ST and gaug
Figure 7.5,
volved with
d compare t
gure 7.3 and
ge record (4
ge record (5
which indic
fluctuating
19
the predicte
d Figure 7.4.
8 hrs)
hrs)
cates that th
tidal level.
6
ed
he
Besid
Figur
the fu
Figure
des, resonan
re 7.6 shows
undamental p
Figure 7.6
e 7.5 Compa
nce of larger
s that freque
period of the
6 Spectra co
72.5 min
34
72.5 min
34 m
39.7 min
39.7 min
arison of spe
r area outsid
encies betwe
e larger sea a
omparison be
min
29 min
25.8
min
23.8
min
2
min
25.8
min
22 m
29 min
n
ectral density
de harbor gen
een 2×10
-4
h
area outside
etween gaug
22 min
20.2 min
18.3 mi
min
20.2 min
18.3 min
y distribution
nerates the
hz and 3×10
Crescent Ci
ge reading an
in
n
n
spikes of lo
0
-4
hz are as
ity harbor.
nd incident w
19
ow frequency
sociated wit
wave
7
y.
th
7
The t
time
Fig
The
calibr
Figur
7.2.2 Los An
tidal gauge
of Chilean e
gure 7.7 Tida
data of inci
rated by buo
re 7.8 Incide
ngeles/Long
in LA/LB P
earthquake-ts
al gauge rec
ident waves
oy records in
ent waves fo
g Beach Port
Port records
sunami on F
ords on 02/2
s is acquire
n deep ocean
or Los Angel
t
water level
Feb. 27
th
, 201
27/2010 in L
d from prop
n. The incide
les/Long Be
l (Station D
10, and it is
LA/LB port (
pagation mo
ent waves are
ach Port (so
Datum) durin
shown as Fi
(source: NOA
odel of MO
e shown in F
urce: Sangy
19
ng the impac
gure 7.7.
AA)
OST, and ar
Figure 7.8.
young Son)
8
ct
re
Simu
respo
Treat
Fouri
ulate oscillat
onse with tid
Figure 7.9
Figure 7.1
t the observa
ier transform
tion the inc
dal gauge rec
Predicted re
0 Predicted
ation, presen
mation (FFT)
coming wav
cords and pre
esponse, solu
d response, so
nt numerical
), as shown i
ves in Figur
ediction by M
ution by MO
olution by M
solution and
in Figure 7.1
re 7.8, then
MOST in Fig
OST and gau
MOST and g
d solution b
11.
n compare t
gure 7.9 and
uge record (4
auge record
y MOST mo
19
the predicte
d Figure 7.10
48 hrs)
(5 hrs)
odel with fa
9
ed
0.
st
In LA
fluctu
at pe
outsid
Figure
A/LB Port, t
uating tides.
riod of 59.5
de the harbo
Figure 7.1
m
e 7.11 Comp
the primary
In the other
5 min, which
or.
12 Spectra c
66
min
59.5 min
66
min
59.5 min
parison of sp
resonant mo
r hand, the en
h indicates t
comparison b
pectral densit
ode keeps fa
nergy conten
the influence
between gau
ty distributio
fairly stable
nt of incomi
e of topogra
uge reading a
on
at 66 min, d
ing waves is
aphy of a la
and incident
20
despite of th
s concentrate
arger sea are
t wave
0
he
ed
ea
7
The t
impa
Figur
The
calibr
Fig
7.2.3 San Di
tidal gauge i
ct time of Ch
re 7.13 Tida
data of inci
rated by buo
gure 7.14 In
iego Harbor
in Crescent
hilean earthq
al gauge reco
ident waves
oy records in
ncident wave
r
City harbor
quake-tsunam
ords on 02/2
are acquire
n deep ocean
es for San Di
r records wa
mi on Feb. 2
7/2010 in Sa
ed from pro
n. The incide
iego harbor
ater level (St
27
th
, 2010, as
an Diego har
opagation m
ent waves are
(source; San
tation Datum
s shown in F
rbor (source
model of MO
e shown in F
ngyoung Son
20
m) during th
Figure 7.13.
e: NOAA)
OST, and ar
Figure 7.14.
n)
1
he
re
Simu
respo
F
Treat
Fouri
ulate oscillat
onse with gau
Figure 7.15
Figure 7.16
t the observa
ier transform
tion with in
uge records
Predicted r
Predicted re
ation, presen
mation (FFT)
ncoming wav
and predicti
response, sol
esponse, solu
nt numerical
), and compa
ves in Figu
on by MOST
lution by MO
ution by MO
solution and
are the spect
ure 7.14, and
T in Figure 7
OST and gau
OST and gaug
d solution b
tra as Figure
d compare
7.15 and Fig
uge record (
ge record (5
y MOST mo
e 7.17.
20
the predicte
gure 7.16.
48 hrs)
hrs)
odel with fa
2
ed
st
Addit
outsid
oscill
F
tionally, the
de harbor. T
lation of the
Figure 7.18
Figure 7.17
e energy con
The spikes a
water body
Spectra com
83.3
min
58.
Compariso
ntent of inco
at 52.9 min
outside San
mparison bet
3
n
58.5
min
52.9 min
45 min
34.
5 min
45 min
34.4 m
on of spectra
oming waves
and 83.3 m
Diego harbo
tween gauge
.4 min
min
al density dis
s represents
min in Figur
or.
e reading and
stribution
resonance o
e 7.18 are i
d incident w
20
of larger are
influenced b
wave
3
ea
by
7.3 T
7
The t
impa
Figur
The
calibr
F
Tsunami Ca
7.3.1 Cresce
tidal gauge i
ct time of To
re 7.19 Tida
data of inci
rated by buo
igure 7.20 I
aused by Jap
ent City Har
in Crescent
ohoku earthq
al gauge reco
ident waves
oy records in
Incident wav
pan Earthq
rbor
City harbor
quake-tsunam
ords on 03/1
are acquire
n deep ocean
ves for Cresc
quake on Ma
r records wa
mi on Mar.
1/2011 in Cr
ed from pro
n. The incide
cent City har
ar. 11
th
, 201
ater level (St
11
th
, 2011, a
rescent City
opagation m
ent waves are
rbor (source
11
tation Datum
as shown in F
y Harbor (sou
model of MO
e shown in F
: Sangyoung
20
m) during th
Figure 7.19.
urce: NOAA
OST, and ar
Figure 7.20.
g Son)
4
he
A)
re
Simu
respo
Treat
Fouri
reson
ulate oscillat
onse with gau
Figure 7.21
Figure 7.22
t the observa
ier transform
nant modes a
tion with in
uge records
1 Predicted
2 Predicted
ation, presen
mation (FFT)
are caused by
coming wav
and predicti
response, so
response, so
nt numerical
), and comp
y the tidal flu
ves in Figur
on by MOST
olution by M
olution by M
solution and
pare the spec
uctuation.
re 7.20, then
T in Figure 7
MOST and ga
MOST and ga
d solution b
ctra as Figur
n compare
7.21 and Fig
auge record (
auge record (
y MOST mo
re 7.23. It sh
20
the predicte
gure 7.22.
(48 hrs)
(5 hrs)
odel with fa
hows that th
5
ed
st
he
In Fig
mode
Redu
tidal
F
gure 7.23, th
e at 20.4 min
uce interval o
level is fine
Figure 7.24
Figure 7.23
he spectrum
n, which is b
of tidal level
enough,. Th
Predicted re
4
m
46.3
min
64.1
min
72.5
min
Compariso
of present n
better than M
ls from 0.7 m
he predicted
esponse, solu
21.9 m
26.5 min
32 min
1.6
min
on of spectra
numerical so
MOST on pr
m to 0.35 m,
responses ar
ution by MO
min
n
20.4 min
al density dis
olution indic
redicting the
, to ascertain
re shown as
OST and gau
stribution
ates the prim
e primary re
n that the dis
Figure 7.24~
uge record (4
20
mary resonan
sonant mode
scretization o
~7.25.
48 hrs)
6
nt
e.
of
Treat
smoo
As in
bigge
repre
Figure 7.25
t the tidal ga
other tidal sh
n Figure 7.2
er tidal inter
sent the fluc
Figu
72.5
min
m
Predicted r
auge record,
hift and solut
6, the smoo
rval, which
ctuating tidal
ure 7.26 Com
32
41.6
min
46.3
min
64.1
min
response, sol
present num
tion by MOS
other tidal sh
means the
l level witho
mparison of
21.9 mi
26.5 min
2 min
lution by MO
merical solut
ST model wi
hift yields a
tidal interv
out numerica
spectral den
in
20.4 min
OST and gau
tion, present
ith fast Four
spectra that
val in this s
al errors.
nsity distribu
uge record (
t numerical
rier transform
t is close to
tudy is sma
ution
20
5 hrs)
solution wit
mation (FFT
the one wit
all enough t
7
th
T).
th
to
Besid
reson
7.5×1
des tidal leve
nance. As in
10
-4
hz ~ 8.5
Figure 7.27
el fluctuation
Figure 7.27
×10
-4
hz are
7 Spectra com
46.3
min
72.5
min
n, the energy
, the frequen
e involved w
mparison be
26.5
32 min
41.6
min
y content of
ncies in the r
with the energ
etween gauge
21.9 min
5 min
f incoming w
ranges of 5×
gy content of
e reading an
waves also im
×10
-4
hz ~ 6.5
f incoming w
nd incident w
20
mpacts harbo
5×10
-4
hz an
waves.
wave
8
or
nd
7
The t
time
Figu
The
calibr
F
7.3.2 Los An
tidal gauge
of Tohoku e
ure 7.28 Tida
data of inci
rated by buo
Figure 7.29
ngeles/Long
in LA/LB P
earthquake-ts
al gauge rec
ident waves
oy records in
Incident wa
g Beach Port
Port records
sunami on M
ords on 03/1
s is acquire
n deep ocean
ave profile fo
t
water level
Mar. 11
th
, 20
11/2011 in L
d from prop
n. The incide
for LA/LB Po
l (Station D
11 as shown
LA/LB port (
pagation mo
ent wave is sh
ort (source:
Datum) durin
n in Figure 7
(source: NOA
odel of MO
hown in Fig
Sangyoung
20
ng the impac
.28.
AA)
OST, and ar
gure 7.29.
Son)
9
ct
re
Simu
soluti
Treat
Fouri
ulate oscillat
ion with gau
Figure 7.30
Figure 7.31
t the observa
ier transform
tion with in
uge records a
0 Predicted r
1 Predicted
ation, presen
mation (FFT)
ncoming wav
and MOST m
response, sol
response, so
nt numerical
), and compa
ve in Figure
model solutio
lution by MO
olution by M
solution and
are the spect
e 7.29, then
on in Figure
OST and gau
MOST and ga
d solution b
tra as Figure
n compare t
e 7.30 and Fi
uge record (
auge record (
y MOST mo
e 7.32.
21
the numerica
igure 7.31.
48 hrs)
(5 hrs)
odel with fa
0
al
st
In LA
fluctu
at per
topog
F
A/LB Port, t
uating tides.
riod of 59.5
graphy of a l
Figure 7.33
Figure 7.3
the primary r
In the other
min, 34.7 m
larger sea are
Spectra com
59.5 min
59.5 min
2 Comparis
resonant mo
r hand, the en
min, 28.2 min
ea outside th
mparison bet
34.7
min
28.2
min
34.7
min
28.2
min
son of spectr
ode keeps fai
nergy conten
n, and 32.6 m
he harbor.
tween gauge
32.6
min
28.2
min
32.6
min
ral density d
irly stable at
nt of incomi
min, which
e reading and
distribution
t 59.5 min, d
ing waves is
indicates the
d incident w
21
despite of th
s concentrate
e influence o
wave
1
he
ed
of
7
The t
impa
Fig
The
calibr
7.3.3 San Di
tidal gauge
ct time of To
gure 7.34 Tid
data of inci
rated by buo
Figure 7.35
iego Harbor
in San Die
ohoku earthq
dal gauge re
ident waves
oy records in
5 Incident w
r
ego harbor r
quake-tsunam
ecords on 03/
are acquire
n deep ocean
wave for San
records wate
mi on Mar.
/11/2011 in
ed from pro
n. The incide
n Diego harb
er level (Sta
11
th
, 2011, a
San Diego h
opagation m
ent wave is sh
bor (source: S
ation Datum
as shown in F
harbor (sourc
model of MO
hown in Fig
Sangyoung S
21
m) during th
Figure 7.34.
ce: NOAA)
OST, and ar
gure 7.35.
Son)
2
he
re
Simu
soluti
F
F
Treat
Fouri
ulate oscillat
ion with gau
igure 7.36 P
Figure 7.37
t the observa
ier transform
tion the inc
uge records a
Predicted res
Predicted re
ation, presen
mation (FFT)
coming wav
and solution
sponse, solut
esponse, solu
nt numerical
), and compa
e in Figure
by MOST in
tion by MOS
ution by MO
solution and
are the spect
e 7.35, then
n Figure 7.3
ST and gaug
OST and gau
d solution b
tra as Figure
n compare th
36 and Figure
ge record (48
uge record (5
y MOST mo
e 7.38.
21
he numerica
e 7.37.
8 hrs)
5 hrs)
odel with fa
3
al
st
Besid
reson
and o
and 3
Fig
F
des tidal leve
nance in term
observed res
3.2×10
-4
hz a
gure 7.39 Sp
Figure 7.38
el fluctuation
ms of wave
sponse are co
are involved
pectra comp
58.5 m
58.5
Comparison
n, the energy
frequencies,
ompared, an
with the ene
arison betwe
min
34.7 min
5 min
34.7 min
n of spectral
y content of
, as Figure 7
nd it shows t
ergy content
een gauge re
density distr
f incoming w
7.39. The sp
that frequen
t of incoming
eading and in
ribution
waves also im
pectra of inc
ncies between
g waves.
ncident wav
21
mpacts harbo
coming wave
n 2.8×10
-4
h
e
4
or
es
hz
215
7.4 Summary
This chapter investigates two strong tsunami events that happened on Feb. 27
th
, 2010, and
Mar. 11
th
, 2011. The incident waves are provided by MOST propagation model and used
for present numerical model. Then, predicted response by present model is compared
with tidal gauge records and solution by MOST model.
The oscillation induced by long waves in three major Californian harbors are studied, and
the wave surface elevation recorded by tide gauge is used as reference to justify the
prediction of present model. In Crescent City, the effect of tide fluctuation and harbor
layout is significant, especially at the spikes between 20 min and 25 min. It is observed
that the multiple resonant modes are commonly present on normal days in Crescent City
harbor, and the magnitude largely increases on tsunami events. The low frequency spike
at 72.5 min is associated with the fundamental period of the water area outside the harbor.
The fairly good match between the present numerical solutions and field records indicate
that the energy content of incident waves impacts harbor oscillation, in addition to the
fluctuating tidal levels. In Los Angeles/Long Beach port, the fundamental periods of
seawater inside and outside harbor are both close to 60 min. Beside, the harbor layout
remains stable at different tide levels, which contributes to the stability of primary
resonant mode in LA/LB port as well. In San Diego harbor, the primary resonant mode
outside is about 58.5 min, which is observed on both Feb. 27
th
, 2010 and Mar. 11
th
, 2011.
Meanwhile, important factors also include the tide fluctuation, harbor layout change, and
energy content of incident waves.
216
CHAPTER 8: CONCLUSION
Harbor oscillation induced by long waves is a complex process in nature, and there are
multiple factors involving the generating of multiple resonant modes or shifted resonant
modes. Therefore, it is crucial to study and understand these factors, which will help
engineers improving harbor design to minimize the potential damages caused by extreme
tsunami events. In this study, numerical analysis is conducted on three well known
harbors in California to investigate their oscillation properties with respect to long
incident waves. The present numerical model is first verified by laboratory experiments
conducted by Lepelletier (1980), and white noise analysis is concentrated to the
oscillation in real harbors. The topography and fluctuating tidal level are taken as
important reasons that lead to the unusual resonant modes. The historical events of Chile
sourced tsunami on Feb. 27
th
, 2010 and Japan sourced tsunami on Mar. 11
th
, 2011 are
used for detail analysis in the present study, and the incoming waves generated by MOST
model is also used for comparison.
The present study is concluded as follow:
1) The present study by Boussinesq-type equation conduct white noise analysis on
four pacific harbors with constant mean tidal level, and the results of primary
resonant mode matches fairly with the earlier study by the modeling of mild slope
equation.
2) The effect of nonlinearity in harbor oscillation does not appear to be significant,
however, the fluctuating tidal level and in the corresponding change of harbor
217
layout influence the resonant modes of harbors. This issue is observed in
historical tsunami events and tide gauge records on normal days.
3) If the harbor layout is changed by the rising or receding tidal level, the resonant
mode of a harbor will be altered. If the harbor layout is not significantly changed
by the changing tidal level, the harbor will retain fairly stable resonant mode.
4) Crescent City harbor indicates different intensity of oscillation on each separate
tidal levels, and the highest intensity occurs with water depth of 1.2 m at tidal
gauge station. Los Angeles/Long Beach port, and San Diego harbor demonstrate
fairly consistent intensity on different tidal levels, and the lower tidal level appear
to be slightly more sensitive.
5) White noise analysis is conducted on Crescent City harbor, and tidal level is set to
continuously fluctuating up and down to imitate the practical tidal levels. The
predicted response in Crescent City harbor demonstrates multiple resonant modes,
which is consistent with tidal gauge records. Fairly stable resonant mode at 60
min is observed in Los Angeles/Long Beach port regardless of the shifted tidal
level, which is also ascertained by tidal gauge records. Different primary resonant
modes are observed, when the tidal level changes in the San Diego harbor.
6) The reasons that caused the unusual resonant modes, in the historical tsunami
events, include the fluctuating tidal level as well as the corresponding changes in
harbor layout, and the energy content of the incoming waves. In this study,
simulated incoming waves are generated by MOST model, which is calibrated by
records of deep ocean buoys. The present study yields a predicted response in
Crescent City harbor fairly matched with tidal gauge records, which proved that
218
these three reasons lead to the multiple resonant modes on Feb. 27
th
, 2010. The
fairly stable resonant mode in LA/LB port is attributable to the stable harbor
layout, regardless of the fluctuating tidal level. The consistency between the
energy content of the incoming waves and the primary resonant mode of LA/LB
port indicates that the topography of larger sea area outside the harbor is
influencing the oscillation as well. In San Diego harbor, the present numerical
solution predicts the primary resonant mode correctly in the tsunami events of
Feb. 27
th
, 2010, however, missed the primary resonant mode in events of Mar.
11
th
, 2011. This indicates that there might be more factors involved in the
oscillation of San Diego harbor, and it will be a good topic for future research to
determine these factors.
219
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Abstract (if available)
Abstract
Long waves may excite harbors to slosh intensively, and may severely damage the ship mooring facilities and threatening lives, especially when waves periods approach to the fundamental periods of the harbor and the ship mooring system. Earlier studies of harbor oscillation were largely focused on the resonance based on constant tidal level and the resulting harbor layout. However, the tsunami events that occurred on Feb. 27th, 2010 and Mar.11th, 2011 generated unusually more spikes in wave spectrum in the Crescent City harbor, and in San Diego harbor. Earlier studies noticed this phenomenon, the present study conducts specific frequency domain and time domain analysis to investigate the reasons that lead to these spectral spikes in connection with resonant behavior of the harbor basin. ❧ The present study proceeds in 5 phases, which are model verification, study of harbor oscillation based on constant mean tidal level, study of harbor oscillation based on five separate tidal levels , study of harbor oscillation with continuously fluctuating tidal levels, and simulation of historical tsunami events with realistic incident wave trains. Each phase is explicated in details to determine the reasons that lead to the unusual resonant modes in historical tsunamis. ❧ One Boussinesq-type model is used and validated by laboratory experiments. This model is used to predict response of harbors under impact of long incident waves in time domain. Three major harbors in California and one harbor in American Samoa are studied with white noise analysis on constant mean tidal level. The predicted responses at tidal gauge station are transformed into spectra, which matches fairly with the primary resonant mode simulated by mild slope equation in frequency domain simulation. The present study compares the time domain analysis with the frequency domain analysis to complement the understanding of harbor response. ❧ The fundamental period is observed to be 22 minutes in Crescent City harbor, 60 minutes in Los Angeles/Long Beach harbor, and 273 minutes in San Diego harbor, based on constant mean tide level. In some historical cases, however, the resonant periods are not the same as earlier predicted. For example, Crescent City harbor shows multiple spectral spikes in tsunami event on Feb. 27th, 2010 from Chile source and in tsunami event on Mar. 11th, 2011 from Japan source. The fluctuating tidal level as well as the corresponding change of harbor layout are two important reasons, whereas the energy content of incoming waves also influence harbor oscillation. The present study takes state of art process to consider the change of harbor layout due to the fluctuated tidal level, and proves it as one of the reasons for some of the multiple spectral spikes. This phenomenon is ascertained by tidal gauge records on normal days without tsunamis events. ❧ The data from the tide gauge records are used in present study to validate numerical model and to prove the hypothesis. The reasons of the multiple resonant modes in Crescent City harbor, during the tsunami events of 2010 and 2011, are proved to be the fluctuating tidal level with corresponding change of harbor layouts, and the fundamental period for the larger region including continental shelf (72.5 min). The resonant mode of Los Angeles harbor keeps fairly stable, and the topography of larger area outside the harbor also influence the incoming waves. San Diego demonstrates different primary resonant modes at different tide level, but the fundamental period for the larger sea area is observed to be 58.5 min. ❧ The present Boussinesq-type model is crosschecked with earlier study by mild slope equation on constant tide level, and the agreement of both results indicate the nonlinear effect in harbor oscillation does not appear to be significant. The movement of tidal level will alter the fundamental period in harbors, through the changing bathymetry and the associated layout of harbors. In Crescent City harbor, the tide level impacts response intensity, and smaller water depth will cause response of larger amplification. In Los Angeles/Long Beach port and San Diego harbor, the response amplitude remains stable on different tide levels. White noise analysis with tide fluctuation demonstrates multiple spectral spikes between 20 min and 25 min in Crescent City harbor, whereas the spikes of lower frequencies are due to the fundamental period of larger sea area outside the harbor as well as the energy content of the incoming waves. It has been noticed that the multiple spectral spikes occur on normal days also, which means this phenomenon generally exists in harbor oscillation. The spectra shows larger energy magnitude on tsunami events than on normal days. The simulation with MOST generated incident waves fairly matches with the records by tide gauge station. Therefore, the combined effects of fluctuated tide level, change of harbor layout, fundamental period of larger sea area outside harbor, and the energy content of incoming waves all lead to the multiple spectral spikes on normal days and on tsunami events.
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Creator
Lu, Shentong
(author)
Core Title
Numerical analysis of harbor oscillation under effect of fluctuating tidal level and varying harbor layout
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Civil Engineering
Defense Date
08/14/2014
Publisher
University of Southern California
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harbor layout,harbor oscillation,OAI-PMH Harvest,tide
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), Lynett, Patrick J. (
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