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Oscillations of semi-enclosed water body induced by hurricanes
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Oscillations of semi-enclosed water body induced by hurricanes
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Content
OSCILLATIONS OF SEMI-ENCLOSED WATER BODY INDUCED BY
HURRICANES
by
Yuan-Hung Paul Tan
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(CIVIL ENGINEERING)
December 2010
Copyright 2010 Yuan-Hung Paul Tan
ii
Table of Contents
List of Tables iv
List of Figures v
Abstract xviii
Chapter 1: Introduction 1
1.1 Background 1
1.2 Objective of the Present Study 7
1.3 Scope of the Present Study 9
Chapter 2: Literature Survey 10
2.1 Studies Related to Modeling Shallow-Water Flows
with Finite-Volume Method 10
2.2 Role of Eddy Viscosity in Shallow-Water Equations 15
Chapter 3: Theoretical Analysis 21
3.1 Governing Equation 21
3.2 Pressure and Wind Fields 24
3.3 FVM Scheme 27
3.4 Boundary and Initial Conditions 33
Chapter 4: Presentation and Discussion of Results 35
4.1 Meteorological Background 35
4.2 Geographic Background 38
4.3 On-Site Measurement Data 42
4.4 Verification of Numerical Model 50
4.5 Applications of Numerical Model 69
4.5.1 Original Hurricane Katrina (Route 1) 71
4.5.2 Hurricane Katrina Traveling Along Route 2 104
4.5.3 Hurricane Katrina Traveling Along Route 3 137
4.5.4 Hurricane Katrina Traveling
With Reduced Forward Speeds 172
4.6 Risk-Based Design and Analysis 206
iii
Chapter 5: Conclusions 209
5.1 Summary of Model Verification 209
5.2 Major Findings from Applications of the Present
Model to Synthetic Hurricanes 212
5.2.1 Synthetic Hurricane No. 1 212
5.2.2 Synthetic Hurricane No. 2 214
5.2.3 Synthetic Hurricane No. 3 215
5.2.4 Synthetic Hurricane No. 4 216
References 219
iv
List of Tables
Table 4.1 Characteristics of Hurricane Katrina Required in
Numerical Simulations 52
Table 4.2 Characteristics of Hurricane Katrina Required in
Numerical Simulations 174
v
List of Figures
Figure 1.1 2-D View of Hurricane (Survey of Meteorology at
Lyndon State College) 4
Figure 1.2 3-D View of Hurricane (Survey of Meteorology at
Lyndon State College) 5
Figure 3.1 Vertical Section of Hurricane (modified from Miller &
Thompson, 1970) 24
Figure 3.2 A Typical CV and the Notation used for a Cartesian 2D Grid 29
Figure 4.1 A Satellite Image of Hurricane Katrina (adopted from NOAA) 36
Figure 4.2 The Storm Path of Hurricane Katrina (based on Knabb et al. 2006) 37
Figure 4.3 A Satellite Image of Lake Pontchartrain 39
Figure 4.4 A Satellite Image of New Orleans, Louisiana 40
Figure 4.5 An Aerial View of the Flooding In Part of
the Central Business District 41
Figure 4.6 Flooded I-10/I-610 Interchange and Surrounding of
Northwest New Orleans and Metairie, Louisiana 42
Figure 4.7 Lake Pontchartrain Gages and Other Locations
Referenced in IPET Report 45
vi
Figure 4.8 Gage Hydrographs and Constructed Hydrographs on
Lake Pontchartrain 45
Figure 4.9 Constructed and Interpolated Hydrographs at
Canal Entrances-General View 46
Figure 4.10 Constructed and Interpolated Hydrographs at
Canal Entrances-Detailed View 46
Figure 4.11 Constructed Hydrograph for Lake Pontchartrain at
17
th
Street Canal 47
Figure 4.12 Constructed Hydrograph for Lake Pontchartrain at
Lakefront Airport 48
Figure 4.13 Aerial Photo Showing the 17
th
Street Canal (1), the Orleans
Avenue Canal (2), the London Avenue Canal (3), IHNC (4),
Midlake (5), Bayou Labranch (6), Pass Manchac (7),
and Little Irish Bayou (8) 50
Figure 4.14 Lake Pontchartrain Bathymetry 51
Figure 4.15 Locations of Major Breaches within South Shore of
Lake Pontchartrain 54
Figure 4.16 Computed Hydrograph versus Observed Hydrograph,
17
th
Street Canal 55
Figure 4.17 Computed Hydrograph versus Interpolated Hydrograph,
Orleans Avenue Canal 56
Figure 4.18 Computed Hydrograph versus Interpolated Hydrograph,
London Avenue Canal 57
vii
Figure 4.19 Computed Hydrograph versus Observed Hydrograph,
IHNC-Lakefront Airport 58
Figure 4.20 Computed Hydrograph versus Observed Hydrograph,
Midlake 59
Figure 4.21 Computed Hydrograph versus Observed Hydrograph,
Bayou Labranch 61
Figure 4.22 Estimation of Peak Water Level at Bayou Labranch
Proposed by IPET 61
Figure 4.23 Computed Hydrograph versus Adjusted Observed Hydrograph,
Bayou Labranch 62
Figure 4.24 Computed Hydrograph versus Observed Hydrograph,
Pass Manchac-Turtle Cove 63
Figure 4.25 Map showing USACE Pass Manchac Gage (ID No: 85420)
at Manchac (provided by USACE New Orleans District) 64
Figure 4.26 Computed Hydrograph versus Observed Hydrograph,
Pass Manchac-Manchac 65
Figure 4.27 Computed Hydrograph versus Observed Hydrograph,
Little Irish Bayou 67
Figure 4.28 Map Showing Different Routes of Hurricanes 70
Figure 4.29 Approximate Locations of S-N and W-E cross-sections 71
Figure 4.30 Computed Hydrograph, 17
th
Street Canal 74
viii
Figure 4.31 Computed Hydrograph, Orleans Avenue Canal 75
Figure 4.32 Computed Hydrograph, London Avenue Canal 76
Figure 4.33 Computed Hydrograph, IHNC-Lakefront Airport 78
Figure 4.34 Computed Hydrograph, Midlake 79
Figure 4.35 Computed Hydrograph, Bayou La Branche 81
Figure 4.36 Computed Hydrograph, Pass Manchac-Turtle Cove 82
Figure 4.37 Computed Hydrograph, Little Irish Bayou 84
Figure 4.38 Hydrographs of the S-N cross-section 86
Figure 4.39 Hydrographs of the W-E cross-section 86
Figure 4.40 Contours of WSE at 12:00 am (UTC) August 29, 2005 87
Figure 4.41 Contours of WSE at 01:00 am (UTC) August 29, 2005 87
Figure 4.42 Contours of WSE at 02:00 am (UTC) August 29, 2005 88
Figure 4.43 Contours of WSE at 03:00 am (UTC) August 29, 2005 88
Figure 4.44 Contours of WSE at 04:00 am (UTC) August 29, 2005 89
Figure 4.45 Contours of WSE at 05:00 am (UTC) August 29, 2005 89
ix
Figure 4.46 Contours of WSE at 06:00 am (UTC) August 29, 2005 90
Figure 4.47 Contours of WSE at 07:00 am (UTC) August 29, 2005 90
Figure 4.48 Contours of WSE at 08:00 am (UTC) August 29, 2005 91
Figure 4.49 Contours of WSE at 09:00 am (UTC) August 29, 2005 91
Figure 4.50 Contours of WSE at 10:00 am (UTC) August 29, 2005 92
Figure 4.51 Contours of WSE at 11:00 am (UTC) August 29, 2005 92
Figure 4.52 Contours of WSE at 12:00 pm (UTC) August 29, 2005 93
Figure 4.53 Contours of WSE at 01:00 pm (UTC) August 29, 2005 93
Figure 4.54 Contours of WSE at 02:00 pm (UTC) August 29, 2005 94
Figure 4.55 Contours of WSE at 03:00 pm (UTC) August 29, 2005 94
Figure 4.56 Contours of WSE at 04:00 pm (UTC) August 29, 2005 95
Figure 4.57 Contours of WSE at 05:00 pm (UTC) August 29, 2005 95
Figure 4.58 Contours of WSE at 06:00 pm (UTC) August 29, 2005 96
Figure 4.59 Contours of WSE at 07:00 pm (UTC) August 29, 2005 96
Figure 4.60 Contours of WSE at 08:00 pm (UTC) August 29, 2005 97
x
Figure 4.61 Contours of WSE at 09:00 pm (UTC) August 29, 2005 97
Figure 4.62 Contours of WSE at 10:00 pm (UTC) August 29, 2005 98
Figure 4.63 Contours of WSE at 11:00 pm (UTC) August 29, 2005 98
Figure 4.64 Contours of WSE at 12:00 am (UTC) August 30, 2005 99
Figure 4.65 Computed Hydrograph, 17
th
Street Canal 107
Figure 4.66 Computed Hydrograph, Orleans Avenue Canal 108
Figure 4.67 Computed Hydrograph, London Avenue Canal 109
Figure 4.68 Computed Hydrograph, IHNC-Lakefront Airport 111
Figure 4.69 Computed Hydrograph, Midlake 112
Figure 4.70 Computed Hydrograph, Bayou La Branche 114
Figure 4.71 Computed Hydrograph, Pass Manchac-Turtle Cove 115
Figure 4.72 Computed Hydrograph, Little Irish Bayou 117
Figure 4.73 Hydrographs of the S-N cross-section 118
Figure 4.74 Hydrographs of the W-E cross-section 118
Figure 4.75 Contours of WSE at 12:00 am (UTC) August 29, 2005 120
xi
Figure 4.76 Contours of WSE at 01:00 am (UTC) August 29, 2005 120
Figure 4.77 Contours of WSE at 02:00 am (UTC) August 29, 2005 121
Figure 4.78 Contours of WSE at 03:00 am (UTC) August 29, 2005 121
Figure 4.79 Contours of WSE at 04:00 am (UTC) August 29, 2005 122
Figure 4.80 Contours of WSE at 05:00 am (UTC) August 29, 2005 122
Figure 4.81 Contours of WSE at 06:00 am (UTC) August 29, 2005 123
Figure 4.82 Contours of WSE at 07:00 am (UTC) August 29, 2005 123
Figure 4.83 Contours of WSE at 08:00 am (UTC) August 29, 2005 124
Figure 4.84 Contours of WSE at 09:00 am (UTC) August 29, 2005 124
Figure 4.85 Contours of WSE at 10:00 am (UTC) August 29, 2005 125
Figure 4.86 Contours of WSE at 11:00 am (UTC) August 29, 2005 125
Figure 4.87 Contours of WSE at 12:00 pm (UTC) August 29, 2005 126
Figure 4.88 Contours of WSE at 01:00 pm (UTC) August 29, 2005 126
Figure 4.89 Contours of WSE at 02:00 pm (UTC) August 29, 2005 127
Figure 4.90 Contours of WSE at 03:00 pm (UTC) August 29, 2005 127
xii
Figure 4.91 Contours of WSE at 04:00 pm (UTC) August 29, 2005 128
Figure 4.92 Contours of WSE at 05:00 pm (UTC) August 29, 2005 128
Figure 4.93 Contours of WSE at 06:00 pm (UTC) August 29, 2005 129
Figure 4.94 Contours of WSE at 07:00 pm (UTC) August 29, 2005 129
Figure 4.95 Contours of WSE at 08:00 pm (UTC) August 29, 2005 130
Figure 4.96 Contours of WSE at 09:00 pm (UTC) August 29, 2005 130
Figure 4.97 Contours of WSE at 10:00 pm (UTC) August 29, 2005 131
Figure 4.98 Contours of WSE at 11:00 pm (UTC) August 29, 2005 131
Figure 4.99 Contours of WSE at 12:00 am (UTC) August 30, 2005 132
Figure 4.100 Computed Hydrograph, 17
th
Street Canal 140
Figure 4.101 Computed Hydrograph, Orleans Avenue Canal 142
Figure 4.102 Computed Hydrograph, London Avenue Canal 143
Figure 4.103 Computed Hydrograph, IHNC-Lakefront Airport 145
Figure 4.104 Computed Hydrograph, Midlake 146
Figure 4.105 Computed Hydrograph, Bayou La Branche 148
xiii
Figure 4.106 Computed Hydrograph, Pass Manchac-Turtle Cove 149
Figure 4.107 Computed Hydrograph, Little Irish Bayou 151
Figure 4.108 Hydrographs of the S-N cross-section 153
Figure 4.109 Hydrographs of the W-E cross-section 153
Figure 4.110 Contours of WSE at 12:00 am (UTC) August 29, 2005 154
Figure 4.111 Contours of WSE at 01:00 am (UTC) August 29, 2005 154
Figure 4.112 Contours of WSE at 02:00 am (UTC) August 29, 2005 155
Figure 4.113 Contours of WSE at 03:00 am (UTC) August 29, 2005 155
Figure 4.114 Contours of WSE at 04:00 am (UTC) August 29, 2005 156
Figure 4.115 Contours of WSE at 05:00 am (UTC) August 29, 2005 156
Figure 4.116 Contours of WSE at 06:00 am (UTC) August 29, 2005 157
Figure 4.117 Contours of WSE at 07:00 am (UTC) August 29, 2005 157
Figure 4.118 Contours of WSE at 08:00 am (UTC) August 29, 2005 158
Figure 4.119 Contours of WSE at 09:00 am (UTC) August 29, 2005 158
Figure 4.120 Contours of WSE at 10:00 am (UTC) August 29, 2005 159
xiv
Figure 4.121 Contours of WSE at 11:00 am (UTC) August 29, 2005 159
Figure 4.122 Contours of WSE at 12:00 pm (UTC) August 29, 2005 160
Figure 4.123 Contours of WSE at 01:00 pm (UTC) August 29, 2005 160
Figure 4.124 Contours of WSE at 02:00 pm (UTC) August 29, 2005 161
Figure 4.125 Contours of WSE at 03:00 pm (UTC) August 29, 2005 161
Figure 4.126 Contours of WSE at 04:00 pm (UTC) August 29, 2005 162
Figure 4.127 Contours of WSE at 05:00 pm (UTC) August 29, 2005 162
Figure 4.128 Contours of WSE at 06:00 pm (UTC) August 29, 2005 163
Figure 4.129 Contours of WSE at 07:00 pm (UTC) August 29, 2005 163
Figure 4.130 Contours of WSE at 08:00 pm (UTC) August 29, 2005 164
Figure 4.131 Contours of WSE at 09:00 pm (UTC) August 29, 2005 164
Figure 4.132 Contours of WSE at 10:00 pm (UTC) August 29, 2005 165
Figure 4.133 Contours of WSE at 11:00 pm (UTC) August 29, 2005 165
Figure 4.134 Contours of WSE at 12:00 am (UTC) August 30, 2005 166
Figure 4.135 Computed Hydrograph, 17
th
Street Canal 175
xv
Figure 4.136 Computed Hydrograph, Orleans Avenue Canal 176
Figure 4.137 Computed Hydrograph, London Avenue Canal 178
Figure 4.138 Computed Hydrograph, IHNC-Lakefront Airport 179
Figure 4.139 Computed Hydrograph, Midlake 180
Figure 4.140 Computed Hydrograph, Bayou La Branche 182
Figure 4.141 Computed Hydrograph, Pass Manchac-Turtle Cove 183
Figure 4.142 Computed Hydrograph, Little Irish Bayou 185
Figure 4.143 Hydrographs of the S-N cross-section 187
Figure 4.144 Hydrographs of the W-E cross-section 187
Figure 4.145 Contours of WSE at 12:00 am (UTC) August 29, 2005 188
Figure 4.146 Contours of WSE at 01:00 am (UTC) August 29, 2005 188
Figure 4.147 Contours of WSE at 02:00 am (UTC) August 29, 2005 189
Figure 4.148 Contours of WSE at 03:00 am (UTC) August 29, 2005 189
Figure 4.149 Contours of WSE at 04:00 am (UTC) August 29, 2005 190
Figure 4.150 Contours of WSE at 05:00 am (UTC) August 29, 2005 190
xvi
Figure 4.151 Contours of WSE at 06:00 am (UTC) August 29, 2005 191
Figure 4.152 Contours of WSE at 07:00 am (UTC) August 29, 2005 191
Figure 4.153 Contours of WSE at 08:00 am (UTC) August 29, 2005 192
Figure 4.154 Contours of WSE at 09:00 am (UTC) August 29, 2005 192
Figure 4.155 Contours of WSE at 10:00 am (UTC) August 29, 2005 193
Figure 4.156 Contours of WSE at 11:00 am (UTC) August 29, 2005 193
Figure 4.157 Contours of WSE at 12:00 pm (UTC) August 29, 2005 194
Figure 4.158 Contours of WSE at 01:00 pm (UTC) August 29, 2005 194
Figure 4.159 Contours of WSE at 02:00 pm (UTC) August 29, 2005 195
Figure 4.160 Contours of WSE at 03:00 pm (UTC) August 29, 2005 195
Figure 4.161 Contours of WSE at 04:00 pm (UTC) August 29, 2005 196
Figure 4.162 Contours of WSE at 05:00 pm (UTC) August 29, 2005 196
Figure 4.163 Contours of WSE at 06:00 pm (UTC) August 29, 2005 197
Figure 4.164 Contours of WSE at 07:00 pm (UTC) August 29, 2005 197
Figure 4.165 Contours of WSE at 08:00 pm (UTC) August 29, 2005 198
xvii
Figure 4.166 Contours of WSE at 09:00 pm (UTC) August 29, 2005 198
Figure 4.167 Contours of WSE at 10:00 pm (UTC) August 29, 2005 199
Figure 4.168 Contours of WSE at 11:00 pm (UTC) August 29, 2005 199
Figure 4.169 Contours of WSE at 12:00 am (UTC) August 30, 2005 200
Figure 4.170 Schematic Diagram of Risk-Based Design 207
xviii
Abstract
A numerical study is conducted to simulate the oscillations (storm surges) of semi-
enclosed water body induced by hurricanes. For application using the numerical model
developed in the present study, Lake Pontchartrain (located in southeastern Louisiana) is
chosen as the semi-enclosed water body and Hurricane Katrina (the costliest hurricane in
the history of the United States) is chosen as the hurricane. There are three (3) reasons to
choose Lake Pontcharrain and Hurricane Katrina: 1. Storm surge built up in Lake
Pontchartrain during Hurricane Katrina, 2. Wind drove water into Lake Pontchartrain as
Hurricane Katrina approached from the Gulf of Mexico, and 3. The extensive field data,
gathered by the Interagency Performance Evaluation Task Force (IPET), is available to
provide the needed comparison of numerical result and prototype data on the oscillations
at Lake Pontchartrain induced by Hurricane Katrina.
The depth-average, non-linear shallow-water equations (NLSW) are use as the governing
equations. The finite-volume method (FVM) is employed to solve the governing
shallow-water equations. In order to validate the present model, the hydrographs due to
Hurricane Katrina obtained from the present model are compared with the field data
reported by IPET at eight (8) sites along the shores and the center of Lake Pontchartrain.
These eight (8) sites are: the 17
th
street Canal, the Orleans Avenue Canal, the London
xix
Avenue Canal, the Inner Harbor Navigation Canal (IHNC)-Lakefront Airport, Midlake,
Bayou Labranch, Pass Manchac, and Little Irish Bayou.
The time at which the maximum water surface elevation (WSE) occurs as predicted by
the present model is almost identical to the time at which the maximum water level is
observed at the 17
th
Street Canal, the Orleans Avenue Canal, the London Avenue Canal,
and the IHNC-Lakefront Airport sites. Furthermore, the present model correctly predicts
the general trend of the water level when the hydrographs due to Hurricane Katrina are
compared with the observed hydrographs at the 17
th
Street Canal, the Orleans Avenue
Canal, the London Avenue Canal, the IHNC-Lakefront Airport, and the Midlake sites.
However, the present model only reasonably predicts the general trend of the water level
when the hydrographs due to Hurricane Katrina are compared with the observed
hydrographs at the Bayou La Branche (named Bayou Labranch by IPET), the Pass
Manchac, and the Little Irish Bayou sites.
The present model is further applied to investigate the oscillations at Lake Pontchartrain
induced by four (4) synthetic hurricanes within the time-span of 00:00 UTC August 29,
2005 to 00:00 UTC August 30, 2005: Case 1. Hurricane Katrina tracks on its original
route, Case 2. Hurricane Katrina tracks 36 km west of its original route, Case 3.
Hurricane Katrina tracks 72 km west of its original route, and Case 4. Hurricane Katrina
tracks on its original route with forward speeds reduced by 16% ~ 45% (or altered from
15 km/h ~ 36 km/h to 15 km/h ~ 22 km/h). These are done to assess the impact of
xx
hurricanes under different risk conditions. It is found that much more severe catastrophes
in metro New Orleans and neighboring parishes can be expected under the scenarios of:
Case 2. Hurricane Katrina passes through the east part of New Orleans, Louisiana and
both the east and central parts of Lake Pontchartrain and Case 4. Hurricane Katrina
passes through the regions nearby the east shore of Lake Pontchartrain with reduced
forward speeds.
1
Chapter 1: Introduction
1.1 Background
Higher-than-normal water levels and wave conditions observed during hurricanes are
primarily forced by the wind associated with hurricanes. Wind exerts a shear stress on
the water surface that pushes the water. Wind is very effective in developing the storm
surge in shallow water.
The process that wind changes the water level is called storm surge generation. Storm
surge (oscillation) defined here is the abnormally “Still” high water level induced by the
hurricane. The word “Still” used here is to distinguish the slower rise and fall of the
water surface due to the storm surge/tide that occurs over time scales of hours from the
changes in water surface that occur at much higher frequencies associated with the
continuous up and down water surface motion due to wave motion which occurs over
time scales of seconds and tens of seconds.
The storm surge generated by the hurricane is related to the surface shear stress. The
shear stress generated by the wind associated with hurricane is related to the wind speed
with a highly non-linear relationship. Broad, shallow continental shelf regions are
susceptible for developing storm surge. As wind pushes water, storm surge moves and
2
accumulates as it encounters a coastal land mass or other obstruction. The key
topographic controls along the U.S. coast, such as indentations, irregularities, and
pockets, are particularly susceptible to catching water pushed toward and into these
geographic features by the wind associated with hurricanes.
The Mississippi River delta is holding a coastal land characteristic that acts to catch water
being pushed toward it along the Mississippi and Alabama continental shelves.
Hurricanes in the northern Gulf of Mexico tend to generate winds that blow from the east
in the northern Gulf since they are rotating in the counterclockwise direction. These east
winds push water toward southern Louisiana, approaching the Mississippi River delta.
The city of New Orleans in the State of Louisiana is located in the low-lying Mississippi
River delta, and major portions of the city lie near or below sea level. The greatest
natural threat presented to residents and properties in New Orleans area has been
hurricane-induced storm surges, waves, and rainfall since the founding of the city in
1718. A comprehensive hurricane protection plan was not initiated until Hurricane Betsy
struck the city in 1965, killing 75 people and causing substantial damage and loss of
property. Over time, three (3) hurricane protection projects have been planned and
partially implemented in New Orleans and the Southeast Louisiana region: Lake
Pontchartrain and Vicinity, the West Bank project, and the New Orleans to Venice
project.
3
Lake Pontchartrain is a brackish lake located in southeastern Louisiana. It is the second
largest salt-water lake in the United States (after the Great Salt Lake in Utah) and the
largest lake in Louisiana. It is roughly oval in shape, about 40 miles (64 km) wide and 24
miles (39 km) from south to north. It covers an area of 630 square miles (1630 square
km) with an average depth of 12 to 14 feet (about 4 meters). The south shore forms the
northern boundary of the city of New Orleans. Storm surge can build up in Lake
Pontchartrain during hurricanes. Wind drives water into the lake from the Gulf of
Mexico as a hurricane approaches from the south, and water can spill into New Orleans
from the lake.
In order to protect areas around Lake Pontchartrain from flooding caused by a storm
surge or rainfall associated with a hurricane that would be roughly classified as a fast-
moving ‘Category 3” hurricane, the Lake Pontchartrain and Vicinity hurricane protection
project was authorized under the Flood Control Act of 1965 by Congress. As of May
2005, 125 miles of levees, major flood walls, flood-proofed bridges, and mitigation dike
on the west shore of Lake Pontchartrain were built under this project and the estimated
completion date for the entire project was 2015.
A hurricane is a remarkably well-organized, huge convection system that pumps great
amounts of warm, moist air into high levels of the atmosphere at very rapid rates. Warm,
moist air ascends sharply into the ring between 20 and 80 km of the center. Because of
condensation, the temperature above about 1000 m within this ring increases fiercely
4
toward the “eye” of the hurricane; consequently, the eye is significantly warmer than the
exterior of the hurricane. As the air within this ring rises, new air flows in toward the
center from hundreds of kilometers away. If the air starts out with even a slight rotary
motion, it will spin faster and faster as it nears the center. A graphic illustration of these
physical mechanisms is shown on Figure 1.1.
Figure 1.1 2-D View of Hurricane (Survey of Meteorology at Lyndon State College)
The circulation of a well-developed hurricane extends vertically to 14 or 15 km, almost to
the level of the tropopause, although the intensity of the cyclonic circulation decreases
with height. In the lowest 3 km, a pronounced trend of motion points toward the center
of the hurricane, causing convergence of the air and the ascending motion that leads to
cloud formation. The air flows with an outward fashion above about 7.5 km, and
reaching a maximum rate at 12 km. Frequently, the air flow changes direction drastically
5
in the uppermost layer as it moves outward from the center, and even acquires an
anticyclonic rotation some 130 to 160 km from the center. These phenomenal
descriptions are depicted in Figure 1.2.
Figure 1.2 3-D View of Hurricane (Survey of Meteorology at Lyndon State College)
Hurricane Katrina was formed over the Bahamas on August 23, 2005, and crossed
southern Florida as a moderate Category 1 hurricane. It then strengthened rapidly in the
Gulf of Mexico and became one of the strongest hurricanes on record while at sea. The
hurricane weakened before making its second and third landfalls as a Category 3 storm
on the morning of August 29 in southern Louisiana and at the Louisiana/Mississippi state
line, respectively. Hurricane Katrina was the costliest and one of the five deadliest
hurricanes in the history of the United States. It was the sixth-strongest Atlantic
6
hurricane ever recorded and the third-strongest hurricane on record that made landfall in
the United States.
During Hurricane Katrina, the storm surge generated by wind exceeds 15 feet
(approximately 4.6 meter) in places along the southern Louisiana coast and exceeds 20
feet (approximately 6.1 meter) in places along the Mississippi coast. It devastated the
Mississippi cities of Waveland, Bay St. Louis, Pass Christian, Long Beach, Gulfport,
Biloxi, Ocean Springs, and Pascagoula along the Gulf Coast. In Louisiana, the federal
flood protection system in New Orleans failed in more than 50 places. Nearly every
levee in metro New Orleans breached as Hurricane Katrina passed east of the city,
subsequently flooding 80% of the city and many areas of neighboring parishes for weeks.
At least 1,836 people lost their lives in Hurricane Katrina and in the subsequent floods,
making it the deadliest U.S. hurricane since 1928 Okeechobee Hurricane striking the
Leeward Island, Puerto Rico, the Bahamas, and Florida on September 1928. The
hurricane is estimated to have been responsible for $90.3 billion (2010 U.S. dollars) in
damage, making it the costliest natural disaster in U.S. history. Approximately half of the
direct economic losses, excluding public and utilities infrastructure, can be associated
with breaching of levees and floodwalls.
7
1.2 Objective of the Present Study
The hurricane-induced oscillation (storm surge) of bays, harbors, and lakes can have a
direct effect on shipping and design of flood protection system for beach and coastal
communities. Inundation in both estuarine tidal flats and riverine flood planes due to the
storm surge not only causes casualties and property damages but also affects the
deposition and erosion of sediments in the coastal areas. Predictions of flooding due to
storm surge, dam breaching, or levee overtopping are crucial for planning of emergency
response.
The shallow-water equations are generally applied to simulate overland flow, lake and
river hydrodynamics, long wave run-up, and coastal and estuarine circulations.
Researchers have developed various analytical and numerical models based on the depth-
averaged, shallow-water equations to describe these phenomena. Although analytical
techniques provide exact solutions for idealized geometry and offer insights into the
physical phenomena, numerical methods, conversely, provide approximate solutions in
more general settings suitable for many practical applications.
The finite-volume method (FVM) solves the integral form of the shallow-water equations
in computational cells. The shallow-water equations in the integral form apply to each
computational cell, as well as to the solution domain as a whole. After summing up
equations for all computational cells, the mass and momentum conservations can be
8
achieved in the entire domain. Therefore, global conservation is built into the method
and this provides one of its principal advantages.
The major objective of this research is to investigate the oscillations of semi-enclosed
water body induced by hurricanes. The depth-averaged, non-linear shallow-water
equations (NLSW) are used to analyze storm surge (oscillation) in a semi-enclosed lake
induced by a hurricane. Because conservation of mass and momentum is crucial in
simulating the oscillations in a semi-enclosed lake induced by strong winds, the finite-
volume method (FVM) is used to solve the depth-averaged, non-linear shallow-water
equations in this study. The extensive field data available from Lake Pontchartrain area
are used for the comparison with the computational results generated from the present
numerical model. Therefore, the water surface elevations (WSE) calculated by the
present numerical model at various locations along and in Lake Pontchartrain are verified
by the water surface elevations (WSE’s) corresponding to these locations estimated or
measured by the local, state, and federal agencies during Hurricane Katrina. The
essential-meteorological data to re-generate Hurricane Katrina and the field-observatory
and the instrument-recorded water surface elevations (WSE’s) at Lake Pontchartrain are
obtained from the “Performance Evaluation of the New Orleans and Southern Louisiana
Hurricane Protection System” report dated June 1, 2006 made by the Interagency
Performance Evaluation Task Force (IPET). After the validity of the computational
results is complete, the present model is further applied to simulate the oscillation
9
phenomena happening in Lake Pontchartrain induced by four (4) synthetic hurricanes,
including Hurricane Katrina.
1.3 Scope of the Present Study
Chapter 2 presents studies using the FVM to solve the depth-averaged, non-linear
shallow-water equations (NLSW). The derivation of the FVM model to simulate the
wind-induced oscillations in a semi-enclosed lake governed by the depth-averaged, non-
linear shallow-water equations (NLSW) is presented in Chapter 3. In the first part of
Chapter 4, the present model is verified through the comparison of the simulated
hydrographs with the measured hydrographs for eight (8) distinct sites along the shores
and the center of Lake Pontchartrain as Hurricane Katrina progressed over the Southeast
Louisiana region. In the second part of Chapter 4, the 24-hour contours of the WSE in
entire Lake Pontchartrain computed by the present model are used to investigate the
oscillation phenomena in Lake Pontchartrain induced by wind generated by four (4)
synthetic hurricanes, including Hurricane Katrina. The conclusions of this research are
stated in Chapter 5.
10
Chapter 2: Literature Survey
2.1 Studies Related to Modeling Shallow-Water Flows with Finite-
Volume Method
Several numerical schemes are available to solve the depth-averaged, non-linear shallow-
water equations (NLSW). There are three (3) widely used methods: the finite-difference
method (FDM), the finite-element method (FEM), and the finite-volume method (FVM).
FVM becomes more popular in solving the depth-averaged, non-linear shallow-water
equations (NLSW) in recent years. In this research, FVM is used because of the
following merits:
1. FVM can be considered as a FDM applied to the differential form of the
conservation equation while FVM itself is based on the integral form of the
conservation equation.
2. The computational effect needed for FVM is less than that for FEM.
3. The mass and momentum can be conserved by discretization of the integral form
of the conservation equations.
Zhao et al. (1994) presented a FVM model simulating two-dimensional river-basin flow
governed by the depth-averaged shallow-water equations. This two-dimensional
unsteady-flow model, called RBFFVM-2D, uses the FVM with Osher scheme (a method
11
based on characteristic theory and a monotone upwind high resolution numerical scheme)
by solving a Riemann problem. The river-basin flow is subdivided by unstructured grids
using a combination of either triangular elements or quadrilateral elements. Since Osher
scheme is an explicit scheme, the model (named RBFFVM-2D) suffers from the
requirement of small computation time steps, which depend on the Courant-Friedrichs-
Lewy (CFL) condition (or simply called Courant Condition) for numerical stability.
Also, Osher scheme is only 1
st
order accurate in terms of truncation error and
consequently the model introduces some numerical damping.
Zhao et al. (1996) presented three approximate Riemann solver schemes based on the
characteristic theory: the flux vector splitting (FVS), the flux difference splitting (FDS),
and Oscher scheme, which are used in the FVM for solving the two-dimensional shallow
water equations. Since all of these algorithms are formulated as explicit schemes, they
suffer from the requirement of small computation time steps as dictated by CFL (or
Courant) condition for numerical stability. When the grid was refined, it was necessary
to reduce the time-step size also, but the relationship is not linear. The analysis also
indicated that the solutions were sensitive to the abrupt change of the bottom elevation.
Thus, when these schemes are applied, the large bed slope between elements should be
avoided or some special treatments for the bed slope term may be needed.
Mingham and Causon (1998) presented a high-resolution Godunov-type FVM for solving
the two-dimensional shallow-water equations. The second-order accuracy method uses
12
Monotonic Upstream Schemes for Conservation Laws (MUSCL) reconstruction and a
simple but robust HLL-type (Harten-Lax-van Leer) approximate Riemann solver.
Mingham and Causon claim that this method is generally simpler to implement than
FVMs based on FVS or FDS approaches and it can be implemented on an arbitrary
curvilinear boundary-conforming mesh in order to map complex topography. Mingham
and Causon also claim that this model can be used for steady or unsteady flow
simulations.
Hu et al. (1998) presented a high-resolution finite volume hydrodynamic solver for open-
channel flow governed by the two-dimensional shallow-water equations. A Godunov-
type upwind scheme is used for the convective inviscid terms where most of the
numerical problems arise. Second-order accuracy is achieved by using Monotonic
Upstream Schemes for Conservation Laws (MUSCL) reconstruction in conjunction with
a Hancock two-stage scheme for the time integration. An efficient HLL-type (Harten-
Lax-van Leer) approximate Riemann solver has been used instead of the more expensive
exact Riemann solver. Hu et al. claim that this scheme is robust and capable of
simulating supercritical flows and capturing hydraulic jumps. Hu et al. also claim that
this scheme introduce little spurious artificial viscosity and has excellent numerical
stability.
Hu et al. (2000) presented a finite volume solver together with a Godunov-type upwind
scheme. The robust HLL-type approximate Riemann solver has been used instead of the
13
more expensive exact Riemann solver. The model, named AMAZON, is based on
solving the non-linear shallow-water (NLSW) equations. This finite volume model, Hu
et al. claim, is capable of simulating storm waves propagating in a coastal surf zone and
overtopping a sea wall. Hu et al. claim that the advantages of their NLSW model are that
it is topographically flexible compared to an empirical model and computationally
efficient compared to a three-dimensional model for solving the Navier-Stokes equations.
Based on the results from their tests, Hu et al. also claim that a finite volume
implementation permits the use of a coarse grid foreshore and fine grid onshore for
maximum computational efficiency.
Bradford and Sanders (2002) presented a FVM model developed for unsteady, two-
dimensional, shallow-water flow over arbitrary topography with lateral boundaries
caused by flooding or recession. This model uses Roe’s approximate Riemann solver to
compute fluxes, while the MUSCL and Predictor-Corrector time stepping are used to
provide a 2
nd
order accuracy solution that is free from spurious oscillation. Bradford and
Sanders affirm that the FVM coupled with MUSCL data reconstruction and a Riemann
solver to compute the interfacial fluxes is an accurate and robust approach for solving the
shallow-water equations. Bradford and Sanders claim that their proposed model has been
successfully applied to the dry bed dam-break problem as well as long wave run-up in
one and two-dimensions, which are among the most difficult problems with moving
dry/wet boundaries.
14
Wei et al. (2006) presented a two-dimensional, well-balanced finite-volume model for
run-up of long waves under non-breaking and breaking conditions. Their model uses the
surface-gradient method and a Godunov-type scheme with an exact Riemann solver to
track the moving waterline and to capture flow discontinuities associated with bores or
breaking waves, which are essential for run-up calculations. Furthermore, their model
uses an explicit second-order splitting scheme for the time integration and achieves 2
nd
order accuracy in space through a piecewise linear interpolation of conserved variables
and this approach provides good shock-capturing capability as well as accurate
descriptions of the flow near the moving waterline. Wei et al. claim that their model
provides accurate predictions of non-breaking and breaking wave run-up and has
potential applications in flood hazards mitigation.
Among these previous studies, turbulent viscosity terms, i.e. u
2
T
∇ ν , are cancelled out
from the governing shallow-water equations except that Hu et al. (1998) kept these terms
in their model. During the verification of their model, turbulent viscosity terms were no
longer taken into account because of the physical mechanisms of their test problems. It is
necessary to examine the role of turbulent viscosity terms in the shallow-water equations,
to demonstrate the reasons to eliminate them, to validate their importance in this
proposed research, and further to search either available empirical formulae or available
turbulence models according to physical characteristics of eddy viscosity,
T
ν , to
15
compute u
2
T
∇ ν whenever solving the non-linear, depth-averaged shallow-water
equations (NLSW).
2.2 Role of Eddy Viscosity in Shallow-Water Equations
Turbulent viscosity terms, i.e. u
2
T
∇ ν , represent the momentum exchange and energy
dissipation resulting from molecular diffusion, turbulent diffusion, vertical variation of
horizontal velocity, and non-uniformity of the velocity distribution over the horizontal
plane.
The concept of eddy viscosity (or eddy diffusivity) was proposed by Boussinesq at 1877
dy
dU
uv
T
ν = −
(2.1)
where
j i
u u ρ − is called the Reynolds stresses and the eddy viscosity (or turbulent
exchange coefficient for momentum) can be defined as
m T
l u ~ ′ ν
(2.2)
16
where u′ is a typical scale of the fluctuating velocity, and
m
l is the mixing length, defined
as the cross-stream distance traveled by a fluid particle before it gives up its momentum
and loses identity.
The turbulent stress in the non-linear, depth-averaged shallow-water equations is
composed of three (3) parts:
1. Molecular viscosity stress is small in magnitude except in a very thin layer.
2. Horizontal turbulent normal stresses (
xx
τ and
yy
τ ) come from integrating the
three-dimensional Navier-Stokes equations over time to get the three-dimensional
Reynolds equations.
3. Horizontal turbulent shear stresses (
yx
τ etc.) come from integrating the three-
dimensional Reynolds equations over depth to get the non-linear, depth-averaged
shallow-water equations.
These terms play an important role in the shallow-water equations because:
1. As an internal resistance to the flow, they dissipate energy and consequently are
favorable for stabilizing both physical and numerical solutions.
2. Whenever used together with the convective term, simulation of vortices and
circulations becomes possible.
17
Most numerical models solving the depth-averaged, non-linear shallow-water equations
(NLSW) completely neglect turbulent viscosity, or include it only in the bottom friction
term. The main reason is that turbulent viscosity predominantly originates from
disturbances appearing at the top and bottom interfaces, which have been accounted for
by surface wind stress
η
τ and bottom stress
h −
τ .
The general form of the momentum equation is:
u p u u
t
u
Dt
u D r r r
r r
∆ µ ρ ρ ρ + −∇ = ∇ ⋅ +
∂
∂
= (2.3)
Then we can take curl of (2.3) to get the general form of the vorticity equation:
( ) ϖ ∆ ν
ρ
ϖ r r r
r
+
∇ × −∇ = ∇ ⋅ × ∇ +
∂
∂
p
1
u u
t
(2.4)
The second term in (2.4), ( ) u u
r r
∇ ⋅ × ∇ , can be rewritten as follows:
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( ) ( )u u
u u u u u u u
2
1
u u
r r r r
r r r r r r r r r r r r r r
∇ ⋅ − ∇ ⋅ =
∇ ⋅ − ∇ ⋅ + ⋅ ∇ + ⋅ ∇ − = × × ∇ − ⋅ ∇ × ∇ = ∇ ⋅ × ∇
ϖ ϖ
ϖ ϖ ϖ ϖ ϖ
(2.5)
18
Thus, we can obtain the general form of the vorticity-transport equation:
ϖ ∆ ν ϖ ϖ
ϖ ϖ r r r r r
r r
+ ∇ ⋅ = ∇ ⋅ +
∂
∂
= u u
t Dt
D
(2.6)
u
r r
∇ ⋅ ϖ is called the vortex stretching term. For two-dimensional flow, this term is
vanquished. Finally, the general form of the two-dimensional vorticity-transport equation
is:
ϖ ∆ ν
ϖ r
r
=
Dt
D
(2.7)
Since no physical mechanism of vortex stretching would exist in two-dimensional flow,
according to (2.7), turbulence can no longer be preserved. Furthermore, since turbulent
viscosity in the two-dimensional, non-linear shallow-water equations has a depth-
averaging sense, its value is more or less different from that in the three-dimensional
flow. However, the relevant law has not yet been fully formulated.
Stansby (2003) investigated the influence of horizontal diffusion for a range of
recirculating wake flows. He applied the three-dimensonal shallow-water equations in
(partially) conservative form with the assumption of hydrostatic pressure, which is
assumed to be justified for bed (and free-surface) topographies of small slope. A
staggered mesh is used within a finite-volume approach. In the momentum equations,
19
second-order Crank-Nicolson time stepping is used for surface elevation gradient terms
to obtain the horizontal velocities and fully implicit time-stepping is used for vertical
diffusion. The stepping for advection and horizontal diffusion is treated explicitly, to
second-order accuracy, using the Adams-Bashforth scheme. The QUICK (Quadratic
Upwind Interpolation) scheme is used for the spatial discretization of advection.
The basic hypothesis, as Stansdy states, is that vertical turbulent length scales are smaller
than the horizontal scales. The mixing-length approach for boundary-layer definition in
the vertical is extended to the horizontal by assuming that there is a horizontal mixing
length which is a constant multiple of the vertical value at a given elevation, thus giving
an eddy viscosity based on two scales. Stansby also states that an assumption of
turbulence modeling is that the turbulence length scales are smaller than the larger scale
flow structures which are computed directly.
In conclusion, Stansby states that horizontal mixing affects the vertical variation of
velocity, which in turn affects bed shear. Furthermore, Stansby claims that horizontal
mixing causes the friction coefficient to be increased where vorticity is present.
Therefore, dispersion is either omitted or a standard vertical variation of velocity is
assumed which can not take into account horizontal diffusion. However, Stansby claims
that flows with stable wakes or strong vortex shedding are relatively insensitive to
horizontal diffusion and suitably calibrated depth-averaged models can be a useful role
with the advantage of being very computationally efficient.
20
In this research, the wind-induced oscillation in a lake is modeled using the depth-
averaged, non-linear shallow-water equations and the wind-shear stresses imposed on the
surface of the lake is the dominant forcing mechanism to cause the oscillation in the lake;
hence, this wind-driven shear flow in a lake will be highly-turbulent and consequently it
is necessary not to eliminate the turbulent viscosity terms, i.e. u
2
T
∇ ν , in the non-linear,
depth-averaged shallow-water equations, as opposite to other numerical models for
solving the non-linear, depth-averaged shallow-equations. In order to simulate the
physical characteristics of the oscillation governed by the wind-driven shear flow in a
lake in a more realistic sense, the eddy viscosity,
T
ν , used in the present study is a time-
variant variable (10 ~ 100 s m
2
) instead of a commonly-used constant (100 s m
2
, see
Kundu & Cohen (2002) and Tan (1992)) imposed in the turbulent viscosity terms, i.e.
u
2
T
∇ ν .
21
Chapter 3: Theoretical Analysis
In this research, the integral form of the depth-averaged, non-linear shallow-water
equations (NLSW) is used to model the wind-induced oscillation. Because the nonlinear
shallow-water equations representing the physical mechanisms of the induced oscillation
in an arbitrary shaped lake are solved in this study, it is not feasible to use the analytical
techniques for solving a system of nonlinear partial differential equations in a complex
domain. A numerical scheme, named the finite-volume method (FVM), will be used in
this study because:
1. The depth-averaged shallow-water equations are nonlinear.
2. The solution domain is geometrically complex.
3. The conservation of mass and momentum is crucial.
3.1 Governing Equations
In this research, the depth-average shallow-water equations are used to analyze the
physical mechanisms of the wind-induced oscillations in semi-enclosed water bodies:
( ) [ ] ( ) [ ] 0 v h
y
u h
x t
= +
∂
∂
+ +
∂
∂
+
∂
∂
η η
η
(3.1)
22
( ) ( )
( ) η ρ
τ τ
ν
ρ
η
η
+
−
+
∂
∂
+
∂
∂
+
∂
∂
−
∂
∂
− = −
∂
∂
+
∂
∂
+
∂
∂
−
h y
u
x
u
x
r p 1
x
g fv
y
u
v
x
u
u
t
u
h
x x
2
2
2
2
T
a
(3.2)
( )
( )
( ) η ρ
τ τ
ν
ρ
η
η
+
−
+
∂
∂
+
∂
∂
+
∂
∂
−
∂
∂
− = +
∂
∂
+
∂
∂
+
∂
∂
−
h y
v
x
v
y
r p 1
y
g fu
y
v
v
x
v
u
t
v
h
y y
2
2
2
2
T
a
(3.3)
in the Cartesian Coordinate system, where = η water surface elevation above mean water
surface; = h water depth below mean water surface. ( ) v , u are the depth-averaged
horizontal velocity components; = ρ water density; ( )= r p
a
atmospheric pressure;
=
T
ν eddy viscosity; ( )
η η
τ τ
y x
, and ( )
h
y
h
x
,
− −
τ τ = the surface wind stress and the bottom drag
components, respectively. f indicates the Coriolis parameter ( ( ) θ Ω sin 2 f = , whereΩ
is the angular velocity of the earth and θ is the latitude); and g is the gravitational
acceleration.
Surface wind stress terms ( )
η η
τ τ
y x
, represent the drag force produced by wind over the
water surface:
2
ay
2
ax ax D a x
w w w C + =ρ τ
η
(3.4a)
23
2
ay
2
ax ay D a y
w w w C + =ρ τ
η
(3.4b)
ay ax
w , w denote wind velocities at x and y coordinates, respectively, =
a
ρ density of air,
and
D
C is the drag coefficient. Garratt’s drag formula (Garratt 1977) is used to calculate
D
C in this study:
( ) ( )
3 2
ay
2
ax
3
a D
10 w w 067 . 0 75 . 0 10 w 067 . 0 75 . 0 C
− −
× + + = × + =
(3.5)
Bottom drag terms ( )
h
y
h
x
,
− −
τ τ have a nonlinear effect of retarding the flow. Since the
bottom turbulent stress is not well understood, the bottom drag can be estimated by an
empirical formula:
2 2
b
h
x
v u u r + =
−
ρ τ
(3.6a)
2 2
b
h
y
v u v r + =
−
ρ τ
(3.6b)
= × =
−3
b
10 6 . 2 r the sea bottom friction coefficient.
24
3.2 Pressure and Wind Fields
A hurricane will harbor an area of sinking air at the center of circulation. This area is
known as the eye of the hurricane. The eye is normally circular in shape and weather in
the eye is normally calm and free of clouds. Both pressure and wind profiles across the
entire hurricane can be meteorologically described in a diagram of the cross-sectional
view of a hurricane (Figure 3.1).
Figure 3.1 Vertical Section of Hurricane (modified from Miller & Thompson, 1970)
An atmospheric pressure field can be developed based either on observation or on
forecast. In this study, we will use a pressure field associated with an ideal hurricane
25
model. Two well-known formulae, Fujita and Takahashi Formulae (Tan 1992), can
estimate the atmosphere pressure at a distance r from the center of a hurricane:
( )
( )
( ) R 2 r 0 ,
R r 2 1
p p
p r p
2
a
≤ ≤
+
−
− =
∞
∞
ο
(3.7)
( ) ( ) ∞ < ≤
+
−
− =
∞
∞
r R 2 ,
R r 1
p p
p r p
a
ο
(3.8)
where =
∞
p the ambient atmospheric pressure; =
ο
p pressure at the center of the
typhoon; and = R radius of maximum wind speed. The pressure field generated by the
combination of these two formulae can yield a reasonable radial pressure distribution
(Zhou and Li, 2005).
26
The total wind field is generated by superposing the convection due to the motion of a
hurricane itself
−
− +
−
− =
R
R r
4
exp V
R
R r
4
exp V V
Y X
π π
(3.9)
and the gradient pressure field
( )
a
a 2
2
p r p
r
4
f
r
2
f
G
ρ
∞
−
+ + − =
(3.10)
In this research, we use an ideal hurricane model in association with the total wind field
presented by (3.9) and (3.10) and the “quiet” character at the eye of the hurricane.
Therefore, the wind velocities at a distance r from the center of a hurricane will be:
( ) . E . R r 0 ,
. E . R
r
w
w
w w
a
ax
am . E . R , ax
≤ ≤ × × =
(3.11)
( ) . E . R r 0 ,
. E . R
r
w
w
w w
a
ay
am . E . R , ay
≤ ≤ × × =
(3.12)
27
( )
( ) ∞ ≤ <
−
−
+ +
−
− =
+
−
− =
∞
r E R
r
dy
r
f
p r p
r
f
c
R
R r
V c
r
dy
G c
R
R r
V c w
a
a
X
X r ax
. . ,
2 4 4
exp
4
exp
2
2
2 1
2 1 ,
ρ
π
π
(3.13)
( )
( ) ∞ ≤ <
−
−
+ −
−
− =
−
−
− =
∞
r E R
r
dx
r
f
p r p
r
f
c
R
R r
V c
r
dx
G c
R
R r
V c w
a
a
Y
Y r ay
. . ,
2 4 4
exp
4
exp
2
2
2 1
2 1 ,
ρ
π
π
(3.14)
where
2
ay
2
ax a
w w w + = and ) w max( w
a am
= ;
1
c and
2
c are empirical coefficients;
X
V
and
Y
V are x- and y-components, respectively, of the velocity of the typhoon center
located at the origin; and = . E . R radius of eye.
3.3 FVM Scheme
The finite-volume method (FVM) is applied to the integral form of the shallow-water
equations as a starting point:
28
( )
∫ ∫ ∫ ∫
∫ ∫ ∫ ∫
Ω Φ
Ω Φ
Ω Ω Ω Ω Ω + ⋅ Φ Γ = Ω + Ω
∂
Φ ∂
Γ
∂
∂
=
⋅ Φ + Ω Φ
∂
∂
= Ω ∂
Φ ∂
+ Ω Φ
∂
∂
S
j j
S
j
j
d q ndS grad d q d
x x
ndS u d
t
d
x
u
d
t
ρ ρ
ρ
ρ
(3.15)
where = Φ conserved variables; = Ω control volume; = S boundary; = n outward normal
vector; = Γ thermodynamic properties; and =
Φ
q sources terms.
The solution domain is subdivided into a finite number of small control volumes (CVs)
by a grid that defines the control volume (CV) boundaries. In this study, we define
control volumes (CVs) by a suitable grid and assign the computational node to the center
of each control volume (CV). The advantage of this approach is that the node value
represents the mean that can have a second order accuracy over the control volume (CV).
The integral shallow-water equations shown by (3.15) apply to each control volume
(CV), as well as to the solution domain as a whole. After we sum up equations for all
control volumes (CVs), the global conservation of mass and momentum can be obtained
since the surface integrals over inner control volume (CV) faces can be cancelled out. A
typical grid structure of the finite-volume method (FVM) is shown on Figure 3.2.
29
Figure 3.2 A Typical CV and the Notation used for a Cartesian 2D Grid
By applying the divergence theorem to (3.15) and summing up all source terms, we can
produce an algebraic equation which relates the variable value at the center of a particular
control volume (CV) denoted by Ω to the variable values at several neighbor control
volumes (CVs)
( )
( )
Φ
+ ⋅ Φ Γ + Φ −
Ω =
Φ
∫
q ndS grad u
dt
d
S
ρ
ρ 1
(3.16)
30
The numbers of equations and unknowns are both equal to the numbers of control
volumes (CVs) so the system is well-posed. The algebraic equation for a particular
control volume (CV) has the following form:
P
l
l l P P
Q A A = +
∑
Φ Φ
(3.17)
where P denotes the center of the control volume (CV) and index l runs over the
boundary surfaces of the control volume (CV) and the system of algebraic equations for
the whole solution domain has the matrix form given by
Q A = Φ
(3.18)
In this research, uniform rectangular control-volumes (CV’s) with dimensions ( ) y , x ∆ ∆ in
a Cartesian grid and a time-step t ∆ are used. In order to obtain the second-order
accuracy in the spatial derivatives, the central-differential scheme (CDS) is applied to the
spatial derivatives. Because time accuracy is of crucial importance in the study of the
wind induced-oscillation (so called storm surge) in a semi-enclosed lake, the second
order accuracy of the trapezoid rule method, named the Crank-Nicolson method, is used
to discretize the “time” coordinate.
31
By applying the Crank-Nicolson method to the shallow-water equations in the form of
(3.16) with central-difference scheme (CDS) for the spatial derivatives, we can obtain:
( ) ( )
( ) ( )
( )
ρ ρ ρ
ρ ρ
t q
y x y
v
x
u
t
y x y
v
x
u
t
n
j i
n
j i
n
j i
n
j i
n
j i
n
j i
n
j i
n
j i
n
j i
n
j i
n
j i
n
j i
n
j i
n
j i
n
j i
n
j i
n
j i
n
j i
n
j i
n
j i n
j i
n
j i
∆ +
∆ Φ + Φ − Φ
Γ
+
∆ Φ + Φ − Φ
Γ
+
∆ Φ − Φ
−
∆ Φ − Φ
−
∆ +
∆ Φ + Φ − Φ
Γ
+
∆ Φ + Φ − Φ
Γ
+
∆ Φ − Φ
−
∆ Φ − Φ
−
∆ + Φ = Φ
Φ
− + − + − + − +
+
−
+ +
+
+
−
+ +
+
+
−
+
+
+
−
+
+ +
2
1 , , 1 ,
2
, 1 , , 1 1 , 1 , , 1 , 1
2
1
1 ,
1
,
1
1 ,
2
1
, 1
1
,
1
, 1
1
1 ,
1
1 ,
1
, 1
1
, 1
,
1
,
2 2
2 2 2
2 2
2 2 2
(3.19)
The above equation can be written as:
t
j , i
1 n
1 j , i N
1 n
1 j , i S
1 n
j , 1 i E
1 n
j , 1 i W
1 n
j , i P
Q A A A A A = + + + +
+
+
+
−
+
+
+
−
+
Φ Φ Φ Φ Φ
(3.20)
where:
( )
2
W
x 2
x 4
u
A
∆ Γ
∆ ρ
− − = (3.21)
( )
2
S
y 2
y 4
v
A
∆ Γ
∆ ρ
− − = (3.22)
32
( )
2
E
x 2
x 4
u
A
∆ Γ
∆ ρ
− = (3.23)
( )
2
N
y 2
y 4
v
A
∆ Γ
∆ ρ
− = (3.24)
( )
S N W E P
A A A A
t
A + + + − =
∆ ρ
(3.25)
Φ − + − +
+ Φ − Φ − Φ − Φ −
Φ
+ + + +
∆ =
q A A A A
A A A A
t
Q
n
j i S
n
j i N
n
j i W
n
j i E
n
j i S N W E
t
j i
1 , 1 , , 1 , 1
, ,
ρ
(3.26)
The term
t
j , i
Q represents an “additional” source term, which contains the contribution
from the previous time step; it remains constant during iterations at the new time step.
The equation can also contain a source term dependent on the new solution, so
t
j , i
Q will
be stored separately.
33
3.4 Boundary and Initial Conditions
Since the currents are generated at rest, we will approximately assume that
0 v u = = everywhere in the lake as the initial condition. The initial water surface
elevation (WSE) denoted as η is set to the hydrostatic height corresponding to the initial
pressure field.
Along the lake shore, the impervious boundary condition (so called wall condition), that
is both no-slip and no-through, is applied, i.e. 0 v u = = . However, there is another
condition that can be directly imposed in a finite-volume method (FVM); the normal
viscous stress is zero at a wall. This can be derived from the continuity equation, e.g. for
a wall at 0 y =
0
y
v
2 0
y
v
0
x
u
wall
H yy
wall
wall
=
∂
∂
= ⇒ =
∂
∂
⇒ =
∂
∂
ν τ
(3.27)
Therefore, the diffusive flux in the v equation at 0 y = is zero. This should be
implemented directly, rather than using only the condition that 0 v = at the wall.
34
At an open boundary, the Dirichlet boundary condition is applied as the WSE at that open
boundary is set to the prescribed hydrostatic height. The shear stress is zero at an open
boundary (O.B.), e.g. at 0 y =
0
y
u
. B . O
=
∂
∂
(3.28)
Therefore, the diffusive flux in the u equation is zero and this should be implemented
directly.
35
Chapter 4: Presentation and Discussion of Results
4.1 Meteorological Background
Hurricane Katrina formed as Tropical Depression Twelve (12) over the southeastern
Bahamas on August 23, 2005 as the results of an interaction of a tropical wave and the
remains of Tropical Depression Ten (10). The system was upgraded to tropical storm
status on the morning of August 24 and at this point, the storm was given the name
Katrina. The tropical storm continued to move towards Florida, and became a hurricane
only two hours before it made landfill between Hallandale Beach and Aventura, Florida
on the morning of August 25. The storm weakened over land, but it regained hurricane
status about one hour after entering the Gulf of Mexico.
The storm rapidly intensified after entering the Gulf, partly because of the storm’s
movement over the warm water of the Loop Current. On August 27, the storm reached
Category 3 intensity on the Saffir-Simpson Hurricane Scale, becoming the third major
hurricane of the season. Katrina again rapidly intensified, attaining Category 5 status on
the morning of August 28 and reached its peak strength at 1:00 p.m. CDT that day, with
maximum sustained winds of 175 mph (280 km/h) and a minimum central pressure of
902 mbar. The pressure measurement made Katrina the fourth most intense Atlantic
hurricane on record at the time. The aerial photo of Hurricane Katrina taken by the
36
National Oceanic and Atmospheric Administration (NOAA) is shown on Figure 4.1. It
can be seen that the enormous extent of Katrina can overlay the northeast part of the Gulf
of Mexico with several states, such as Alabama, Louisiana and Mississippi, along the
Gulf from Figure 4.1.
Figure 4.1 A Satellite Image of Hurricane Katrina (adopted from NOAA)
Katrina made its second landfall at 6:10 a.m. CDT August 29 as a Category 3 hurricane
with sustained winds of 125 mph (205 km/h) near Buras-Triumph, Louisiana. At
landfall, hurricane-forced winds extended outward 120 miles (190 km) from the center
and the storm’s center pressure was 920 mbar. After moving over southeastern Louisiana
37
and Breton Sound, it made its third landfall near the Louisiana/Mississippi border with
the wind speed of 120 mph (195km/h), still at Category 3 intensity.
Katrina maintained strength well into Mississippi, finally losing hurricane strength more
than 150 miles (240 km) inland near Meridian, Mississippi. It was downgraded to a
tropical depression near Clarksville, Tennessee, but its remnants were last distinguishable
in the eastern Great Lakes region on August 31, when it was absorbed by a frontal
boundary. The resulting extra-tropical storm moved rapidly to the northeast and affected
Ontario and Quebec (Knabb et al. 2006). The map showing the origin and finale of
Katrina accompanying with its path is presented on Figure 4.2.
Figure 4.2 The Storm Path of Hurricane Katrina (based on Knabb et al. 2006)
38
4.2 Geographic Background
Lake Pontchartrain is an estuary which connects with the Gulf of Mexico via Rigolets
strait and Chef Menteur Pass into Lake Borgne, and therefore experiences small tidal
changes. It receives fresh water from Tangipahoa, Tchefuncte, Tickfaw, Amite, and
Bogue Falaya Rivers, and from Bayou Lacombe. Lake Maurepas connects with Lake
Pontchartrain on the west via Pass Manchac. The Industrial Canal connects the
Mississippi River with the lake at New Orleans. Bonnet Carre Spillway diverts water
from the Mississippi River into the lake during times of river flooding. The lake was
created 2,600 to 4,000 years ago as the evolving Mississippi River Delta formed its
southern and eastern shorelines with alluvial deposits. The aerial photo showing Lake
Pontchartrain and several important landmarks along and within the lake is presented on
Figure 4.3.
39
Figure 4.3 A Satellite Image of Lake Pontchartrain
New Orleans was established at a Native American portage between the Mississippi
River and Lake Pontchartrain. In the 1920s the Inner Harbor Navigation Canal (IHNC,
so called Industrial Canal locally) in the eastern part of the city opened, providing a direct
navigable water connection, with locks, between the Mississippi River and the lake. In
the same decade, a project dredging new land from the lake shore behind a new concrete
floodwall began and this would result in an expansion of the city into the swamp between
Metairie/Gentilly Ridges and the lakefront. The Lake Pontchartrain Causeway, about 24
miles (39 km) long, was constructed in the 1950s and 1960s, connecting New Orleans
(by way of Metairie) with Mandeville and bisecting the lake in a north-northeast line.
The Causeway is the longest bridge over a body of water in the world. The aerial photo
40
showing the City of New Orleans with surrounding communities taken by the National
Aeronautics and Space Administration (NASA) is presented on Figure 4.4.
Figure 4.4 A Satellite Image of New Orleans, Louisiana
Although Katrina weakened to a Category 3 before making landfall on August 29 (with
only Category 1-2 strength winds in New Orleans on the weaker side of the eye of the
hurricane), the outlying New Orleans East along south Lake Pontchartrain was in the
eyewall with winds, preceding the eye, nearly as strong as Bay St. Louis, Mississippi.
Some canals began leaking at 8 a.m. CDT (Chalmette, Louisiana) and some
levees/canals, designed to withstand Category 3 storms, suffered multiple breaks the
following day, flooding 80% of the city.
41
The walls of the Inner Harbor Navigation Canal (IHNC) were breached by storm surge
via the Mississippi River Gulf Outlet (MRGO), while the 17
th
Street Canal and the
London Avenue Canal experienced catastrophic breaches, even though water levels never
topped their flood walls. Aerial photography suggests that 25 billion gallons (95 billion
liters) of water covered New Orleans as of September 2, which equals about 2% of Lake
Pontchartrain’s volume. It can be seen that New Orleans and the surrounding
communities were severely damaged by the catastrophic floods caused by Hurricane
Katrina from Figures 4.5 and 4.6.
Figure 4.5 An Aerial View of the Flooding In Part of The Central Business District
42
Figure 4.6 Flooded I-10/I-610 Interchange and Surrounding of Northwest New Orleans
and Metairie, Louisiana
4.3 On-Site Measurement Data
An intense performance evaluation of the New Orleans and Southeast Louisiana
hurricane protection system during Hurricane Katrina was conducted by the Interagency
Performance Evaluation Task Force (IPET), a distinguished group of government,
academic, and private sector scientists and engineers who dedicated themselves solely to
this task which is formed shortly after Katrina struck. A nine-volume final report,
designed to provide a detailed documentation of the technical analyses conducted and
their associated findings, was published on June 1, 2006. Volume IV, named The Storm,
in this final report made by the Interagency Performance Evaluation Task Force (IPET)
43
presents the regional hydrodynamic conditions created by Katrina (waves and water
levels). Local waves and water levels, in both maximum conditions and temporal
variation, at the levees and the floodwalls are presented in Volume IV, titled The Storm,
of this final report.
Measured water levels fell into two categories, high water mark measurements that
capture peak water levels and hydrographs which capture the water level as a function of
time. An extensive post-storm effect was undertaken to identify and survey high water
marks following passage of the storm. While certain high water marks capture the peak
water levels well, they contain no information about the temporal variation of water level.
Measured hydrographs are the most reliable source of data for capturing both the
temporal variation and the maximum level. Water level fluctuations were measured with
instruments during the build-up stage of the storm at several sites throughout New
Orleans and Southeast Louisiana region. However, few instruments operated throughout
the storm and most of them failed prior to the peak. Consequently, little measured data
that captures peak conditions is available. At a few sites, photographs and other visual
observations were used to provide information about the temporal variation of water level
to finalize the construction of these recorded hydrographs. These constructed
hydrographs are extremely valuable to study the oscillations along the south shore of
Lake Pontchartrain induced by wind generated by Hurricane Katrina.
44
Time-tagged digital images from the Lake Pontchartrain – New Orleans lakefront were
taken by several individuals during Katrina’s passage. Using these images, logs of
observations, and nearby high water marks, hydrographs of the 17
th
Street Canal entrance
and the New Orleans Lakefront Airport were constructed. Recorded and constructed
hydrographs are presented in the following paragraphs.
A map showing various sites along and in Lake Pontchartrain is presented on Figure 4.7.
Five gauged hydrographs and two constructed hydrographs are presented in Figure 4.8.
Each hydrograph is labeled with a relative locality along and in Lake Pontchartrain as
west, central, or east. The constructed hydrographs are for the 17
th
Street Canal and the
Lakefront Airport, and the gage hydrographs are for Southshore Marina, Little Irish
Bayou, Pass Manchac, and Bayou Labranch. The Midlake Gage was adjusted to North
America Vertical Datum of 1988 (NAVD88) by matching the average of the Pass
Manchac and Bayou Labranch gage hydrographs before the storm. Hydrographs were
constructed for the entrances of Orleans Avenue Canal, London Avenue Canal, and the
IHNC by using the best estimate peak water levels at the entrances of these canals along
with the constructed hydrographs at the 17
th
Street Canal and the Lakefront Airport. The
interpolated hydrographs for the Orleans Canal, London Canal, and IHNC are generally
plotted on Figure 4.9 and are plotted in detail on Figure 4.10.
45
Figure 4.7 Lake Pontchartrain Gages and Other Locations Referenced in IPET Report
Figure 4.8 Gage Hydrographs and Constructed Hydrographs on Lake Pontchartrain
46
Figure 4.9 Constructed and Interpolated Hydrographs at Canal Entrances-General View
Figure 4.10 Constructed and Interpolated Hydrographs at Canal Entrances-Detailed View
47
Gage data defining the time variation of water level during Hurricane Katrina were not
available on the south shore of Lake Pontchartrain in the vicinity of the breaches on 17
th
Street and London Canals or on the Inner Harbor Navigation Canal (IHNC). The time
variation of water level is needed to define the water level at various events during the
hurricane, such as the water level at the time of a floodwall breach. High water marks,
intermediate water marks from photographs, and observations recorded in a log by an
individual are used to construct a hydrograph for the 17
th
Street Canal. The resultant
hydrograph for the 17
th
Street Canal is shown on Figure 4.11.
Figure 4.11 Constructed Hydrograph for Lake Pontchartrain at 17
th
Street Canal
48
Levee District personnel staying in the terminal building of the Lakefront Airport used
digital cameras to record events during the passage of Hurricane Katrina on Monday
August 29, 2005 including the rise and fall of storm surge both inside and outside the
terminal building. The digital photographs were used to identify water level locations
that were subsequently surveyed. The surveyed elevations along with the time stamp on
the digital picture files were used to construct a hydrograph for the Airport location. The
resultant hydrograph for the Lakefront Airport is shown on Figure 4.12.
Figure 4.12 Constructed Hydrograph for Lake Pontchartrain at Lakefront Airport
49
The gauged hydrographs for the Midlake, Bayou Labranch, Pass Manchac, and Little
Irish Bayou are shown in Figure 4.8. The interpolated hydrographs for the Orleans
Avenue Canal and the London Avenue Canal are shown in both Figures 4.9 and 4.10.
The constructed hydrographs for the 17
th
Street Canal and the Lakefront Airport are
shown in Figures 4.11 and 4.12 respectively. These are used to verify the reliability of
the present model by comparing with the computed hydrographs for the 17
th
Street Canal,
the Orleans Avenue Canal, the London Avenue Canal, the Inner Harbor Navigation Canal
(IHNC)-Lakefront Airport, Midlake, Bayou Labranch, Pass Manchac, and Little Irish
Bayou. The detailed descriptions of the implementation of the present model and the
comparison between the measured and the simulated hydrographs for studying the
hurricane-induced oscillation in Lake Pontchartrain will be presented in the next section.
The aerial photo showing the 17
th
Street Canal (1), the Orleans Avenue Canal (2), the
London Avenue Canal (3), the Inner Harbor Navigation Canal (so called IHNC,4),
Midlake (5), Bayou Labranch (6), Pass Manchac (7), and Little Irish Bayou (8) is
presented on Figure 4.13.
50
Figure 4.13 Aerial Photo Showing the 17
th
Street Canal (1), the Orleans Avenue Canal
(2), the London Avenue Canal (3), IHNC (4), Midlake (5), Bayou Labranch (6), Pass
Manchac (7), and Little Irish Bayou (8)
4.4 Verification of Numerical Model
The present model, named FVWATER, is used to study the oscillation in Lake
Pontchartrain induced by wind generated by Hurricane Katrina. The dimensions of the
uniform rectangular control-volumes (CV’s) in a Cartesian grid
are( ) ( ) m m y x 750 , 750 , = ∆ ∆ . The time-step t ∆ is chosen to be 45 seconds. The
computational domain of Lake Pontchartrain used in the verification of the present model
for this study is 60 km from west to east and 37.5 km from north to south and the
approximate covering area of the computational domain corresponding to Lake
51
Pontchartrain and its surround swamps is 1475 km
2
. The bathymetry of Lake
Pontchartrain adopted from the Interagency Performance Evaluation Task Force (IPET)
report is presented in Figure 4.14 and this bathymetry is exclusively used in all the
numerical simulations made by the present model in this study.
Figure 4.14 Lake Pontchartrain Bathymetry
The time-period in the verification processes for the present model is from 12:00 am
UTC (Coordinated Universal Time) August 29, 2005 to 12:00 am UTC August 30, 2005,
or 07:00 pm CDT (Central Daylight Time) August 28, 2005 to 07:00 pm CDT August 29,
2005. During this 24-hours time-period, Hurricane Katrina made two landfalls at
Southeast Louisiana and the boarder of Louisiana/Mississippi, respectively, and passed
52
by the region along the east shore of Lake Pontchartrain. Meanwhile, severe breaches of
floodwalls along Mississippi River in Southeast Louisiana area and major flooding in the
City of New Orleans and surround communities had happened within this 24-hours
period. Hence, the study of the oscillation in Lake Pontchartrain induced by wind
generated by Hurricane Katrina can be concentrated in this 24-hours period.
The wind field inducing the oscillations in Lake Pontchartrain is exclusively caused by
Hurricane Katrina. The numerical typhoon (or hurricane) model named CLIMATE,
based on Equation (3.9) through Equation (3.14) in Chapter 3, is developed along with
the present model in this study. The meteorological data to simulate Hurricane Katrina
between 12:00 am UTC August 29, 2005 and 12:00 am UTC August 30, 2005 are
adopted from the Interagency Performance Evaluation Task Force (IPET) report and are
listed in Table 4.1.
Table 4.1 Characteristics of Hurricane Katrina Required in Numerical Simulations
Date/Time (UTC) Central Pressure (bar) Radius to Maximum Winds (m)
Aug 29 0000 90400 26000
Aug 29 0300 90800 34000
Aug 29 0600 91000 34000
Aug 29 0900 91700 58000
Aug 29 1200 92300 67000
Aug 29 1500 93200 37000
Aug 29 1800 94800 30000
Aug 29 2100 95400 47000
Aug 30 0000 96300 34000
53
Miller and Thompson (1970) stated that the expansion of the eye of the hurricane is
approximately to a time interval of less than an hour for the typical hurricane movement.
In this study, it is reasonable to assume that the diameters of the eye of the simulated
Hurricane Katrina by the numerical hurricane model (named CLIMATE) are the
distances corresponding to a time interval of a half-hour traveling of Hurricane Katrina.
The speeds for the simulated Hurricane Katrina derived from the moving path of
Hurricane Katrina between 12:00 am UTC August 29, 2005 and 12:00 am UTC August
30, 2005 are interpreted from the hourly Latitudes and Longitudes of Hurricane Katrina
recorded in the Interagency Performance Evaluation Task Force (IPET) report.
According to the Volume V, titled The Performance-Levees and Floodwalls, of the
Interagency Performance Evaluation Task Force (IPET) report, there are several breaches
of the floodwalls and levees on the 17
th
Street Canal, the London Avenue Canal, and the
Inner Harbor Navigation Canal (IHNC) during the invasion of Hurricane Katrina. The
diagram showing the locations of these breaches adopted from the IPET report is
presented on Figure 4.15. From Figure 4.15, it can be seen that these breaches are not
within the current computational domain of Lake Pontchartrain. In order to
accommodate the phenomena of both breaches and/or overtopping of floodwalls and
levees along Lake Pontchartrain, the water flows out of Lake Pontchartrain through the
entrances of the 17
th
Street Canal, the London Avenue Canal, and the Inner Harbor
Navigation Canal (IHNC) at the 15
th
hour (or 03:00 pm UTC August 29) of the numerical
simulations performed for the model verification.
54
Figure 4.15 Locations of Major Breaches within South Shore of Lake Pontchartrain
The computed hydrograph (solid black line) obtained from the present model and the
observed hydrograph (red line with star symbol) at the entrance of the 17
th
Street Canal
are presented on Figure 4.16. From Figure 4.16, it is seen that the present model-
computed time when the peak water surface elevation (WSE, so called water level in the
IPET report) happens is almost identical to the observed-time at which the maximum
water level happened at the entrance of the 17
th
Street Canal site. Besides, the difference
of the maximum water level (water surface elevation, WSE) is approximately 0.01 meter
(3.30 m versus 3.29 m). It shows that the present model can correctly predict the general
trend of the rise and fall of the water level at the entrance of the 17
th
Street Canal site.
55
Figure 4.16 Computed Hydrograph versus Observed Hydrograph, 17
th
Street Canal
The computed hydrograph (solid black line) obtained from the present model and the
constructed hydrograph (green line with cross symbol) for the entrance of the Orleans
Avenue Canal are presented on Figure 4.17. It should be mentioned that there is no water
flowing out of Lake Pontchartrain through this location because there is no breach or
overtopping of the floodwalls and levees on the Orleans Avenue Canal during the
invasion of Hurricane Katrina. Here, it is seen that the present model-predicted time
when the peak water level happens is almost identical to the observed-time at which the
maximum water level happened at the entrance of the Orleans Avenue Canal site.
Besides, the difference of the maximum water level (water surface elevation, WSE) is
approximately 0.11 meter (3.27 m versus 3.38 m). It shows that the present model can
56
correctly predict the general trend of the rise and fall of the water level when the
hydrograph due to Hurricane Katrina is compared with the constructed hydrograph for
the entrance of the Orleans Avenue Canal site.
Figure 4.17 Computed Hydrograph versus Interpolated Hydrograph, Orleans Avenue
Canal
The computed hydrograph (solid black line) obtained from the present model and the
constructed hydrograph (purple line with plus symbol) for the entrance of the London
Avenue Canal are presented on Figure 4.18. Here, it is seen that the present model-
predicted time when the peak water level happens is almost identical to with the
observed-time at which the maximum water level happened at the entrance of the London
Avenue Canal site. Although the difference of the maximum water level (water surface
57
elevation, WSE) is approximately 0.18 meter (3.30 m versus 3.48 m), it can still be
claimed that the present model can correctly predict the general trend of the rise and fall
of the water level when the hydrograph due to Hurricane Katrina is compared with the
constructed hydrograph for the entrance of the London Avenue Canal site.
Figure 4.18 Computed Hydrograph versus Interpolated Hydrograph, London Avenue
Canal
The computed hydrograph (solid black line) obtained from the present model and the
observed hydrograph (blue line with circle symbol) for the IHNC-Lakefront Airport are
presented on Figure 4.19. Here, it is seen that the present model-predicted time when the
peak water level happens is almost identical to the observed-time at which the maximum
water level happened at the IHNC-Lakefront Airport site. Although the difference of the
58
maximum water level (water surface elevation, WSE) is approximately 0.36 meter (3.30
m versus 3.66 m), it can still be claimed that the present model can correctly predict the
general trend of the rise and fall of the water level when the hydrograph due to Hurricane
Katrina is compared with the observed hydrograph at the IHNC-Lakefront Airport site.
Figure 4.19 Computed Hydrograph versus Observed Hydrograph, IHNC-Lakefront
Airport
The computed hydrograph (solid black line) obtained from the present model and the
observed hydrograph (light blue line with cross symbol) for the Midlake are presented on
Figure 4.20. According to the IPET report, the Midlake gage stopped operating in the
middle of the storm; hence, the comparison of the computed and the observed
hydrographs can be focused on the times at which the Midlake gage data is still available
59
between 12:00 am August 29 and 12:00 am August 30 2005. From Figure 4.20, it shows
that the present model can correctly predict the general trend of the rise of the water level
prior to the stop-recording of the Midlake gage when the hydrograph due to Hurricane
Katrina is compared with the observed hydrograph at the Midlake site.
Figure 4.20 Computed Hydrograph versus Observed Hydrograph, Midlake
The computed hydrograph (solid black line) obtained from the present model and the
observed hydrograph (purple line with cross symbol) for Bayou La Branche (named
Bayou Labranch in the IPET report) are presented on Figure 4.21. It can be seen from
Figures 4.7 and 4.13 that the location of the Bayou Labranch gage is in the swamp along
the southwest shore of Lake Pontchartrain. In detail, the swamps along the entire
60
southwest shore of Lake Pontchatrain have been assigned into the computational domain
for the current numerical simulations performed by the present model. From Figure 4.21,
it can be claimed that the general trend of the rise and fall of the water level predicted by
the present model is still reasonable when it is compared with the observed hydrograph at
Bayou Labranch site although the differences of the magnitudes between the simulated
and the observed hydrographs are evident. According to IPET, it is possible that the
readings of the Bayou Labranch gage are affected by the fact that the Bayou Labranch
gage (NOAA Station ID: 8762372) is connected to Lake Pontchartrain by a channel
which is about 0.5 mile along. Therefore, the low water surface elevations recorded by
the gage are due to the geographic characteristics of the gage location. Furthermore, IPET
demonstrates that the probable peak water surface elevation (WSE) at Bayou Labranch is
between 7.75 ft and 8 ft (between 2.35 m and 2.45 m, the blue cross on Figure 4.22)
based on the observed high water marks (HWMs) at Frenier and Williams Boulevard (see
Figures 4.7 and 4.22, the red line on Figure 4.22). In order to visualize this statement
presented by IPET, the computed hydrograph (solid black line) obtained from the present
model and the adjusted hydrograph (purple line with cross symbol) according to the
geographic characteristic of the Bayou La Branche gage are presented on Figure 4.23. It
can be seen from Figure 4.23 that the difference between the predicted peak water surface
elevation (WSE) by the present model and the best estimated peak water level by IPET
presented by the adjusted hydrograph will be less than 0.6 m (or 23%); in other words,
the present model can predict reasonable water surface elevations (WSEs) at Bayou La
Branche site.
61
Figure 4.21 Computed Hydrograph versus Observed Hydrograph, Bayou Labranch
Figure 4.22 Estimation of Peak Water Level at Bayou Labranch Proposed by IPET
62
Figure 4.23 Computed Hydrograph versus Adjusted Observed Hydrograph, Bayou
Labranch
The computed hydrograph (solid black line) obtained from the present model and the
observed hydrograph (light blue line with circle symbol) for Pass Manchac are presented
on Figure 4.24. From Figures 4.7 and 4.13, it can be seen that the location of the Pass
Manchac gage (USGS ID No: 301748090200900, named Turtle Cove Environmental
Research Station) is close to the middle of Pass Manchac, the narrow strip of water
connecting Lake Pontchartrain and Lake Maurepas, on the northwest shore of Lake
Pontchartrain. From Figure 4.24, it can be claimed that the general trend of the rise and
fall of the water level predicted by the present model is still reasonable when it is
compared with the observed hydrograph at the Pass Manchac-Turtle Cove site although
the differences of the magnitudes between the simulated and the observed hydrographs
63
are evident. It is possible that these differences are caused by the fact that the detailed
geographical and/or hydraulic conditions affecting the operating the USGS Pass
Manchac-Turtle Cove gage are not applied into the numerical simulations for the present
study.
Figure 4.24 Computed Hydrograph versus Observed Hydrograph, Pass Manchac-Turtle
Cove
In order to verify the accuracy of the present model predicting the water surface
elevations (WSEs) on Pass Manchac, the water levels recorded by Pass Manchac gage
(USACE ID No: 85420) at Manchac have been obtained. The location of USACE Pass
Manchac gage (85420) is shown on Figure 4.25 and the computed hydrograph (solid
64
black line) obtained from the present model and the observed hydrograph (red line with
cross-mark) for USACE Pass Manchac gage are presented on Figure 4.26. According to
the New Orleans District of USACE, the Pass Manchac gage failed in the middle of the
storm; hence, the comparison of the computed and the observed hydrographs can be
focused on the hours when the Pass Manchac gage is still operating. From Figure 4.26, it
shows that the present model can correctly predict the general trend of the rise of the
water level prior to the failure of the Pass Manchac gage when the hydrograph due to
Hurricane Katrina is compared with the observed hydrograph at the west end of Pass
Manchac.
Figure 4.25 Map showing USACE Pass Manchac Gage (ID No: 85420) at Manchac
(provided by USACE New Orleans District)
65
Figure 4.26 Computed Hydrograph versus Observed Hydrograph, Pass Manchac-
Manchac
The computed hydrograph (solid black line) obtained from the present model and the
observed hydrograph (green line with circle symbol) for Little Irish Bayou are presented
on Figure 4.27. According to the IPET report, the Little Irish Bayou gage failed before
high water levels were reached; hence, the comparison of the computed and the observed
hydrographs can be focus on the times at which the Little Irish Bayou gage data is
available. From Figure 4.27, it is seen that the general trend of the rise and fall of the
water level predicted by the present model is not very closed to the general trend of the
rise and fall of the water level because the present model does not include the intruding
water from the Gulf of Mexico through the swamps along the east shore of Lake
Pontchartrain. In detail, the present model can correctly predict the general trend of the
66
rise of the water level between 09:00 am and 02:00 pm UTC August 29, 2005 as it is seen
from Figure 4.27; however, the obvious differences between the computed and observed
hydrographs can be seen when the computed hydrograph obtained from the present
model is compared with the observed hydrograph between 12:00 and 09:00 am at Little
Irish Bayou site. Based on the observational information provided in the IPET report, the
low-land areas between Lake Pontchartrain and the Gulf of Mexico have been inundated
by the storm surges induced by Hurricane Katrina before the start (12:00 am UTC August
29, 2005) of the current computational simulation. In other words, the storm surges from
the Gulf of Mexico had been affecting the rise and fall of the water level at the east part
of Lake Pontchartrain, at which the Little Irish Bayou gage is located, since Hurricane
Katrina was approaching to the Southeast Louisiana. It can be still claimed that the
present model can reasonably predict the general trend of the water level at Little Irish
Bayou site.
67
Figure 4.27 Computed Hydrograph versus Observed Hydrograph, Little Irish Bayou
It is evident that the time at which the maximum water surface elevation (WSE) occurs as
predicted by the present model is almost identical to the time at which the maximum
water level is observed at the 17
th
Street Canal, the Orleans Avenue Canal, the London
Avenue Canal, and IHNC-Lakefront Airport sites. The differences between the
computed and the observed maximum WSE at these four sites are within the range of
0.01 to 0.36 meter (or 0.3% ~ 10%) from Figures 4.16 to 4.19. Furthermore, the present
model can correctly predict the general trend of the water level when the hydrographs due
to Hurricane Katrina are compared with the observed hydrographs at the 17
th
Street
Canal, the Orleans Avenue Canal, the London Avenue Canal, the IHNC-Lakefront
Airport, and the Midlake sites from Figures 4.16 to 4.20. Because the detailed hydraulics
68
influencing the Bayou La Branche (named Bayou Labranch by IPET) gage and the
geographic complexities affecting the operations of the Pass Manchac-Turtle Cove gage
are not included into the current numerical simulations, the general trends of the water
level predicted by the present model are not correct when the hydrographs due to
Hurricane Katrina are compared with the observed hydrographs at these two sites from
Figures 4.21, 4.23, and 4.24. Because the storm surges intruding from Gulf of Mexico
through the swamps along the east shores of Lake Pontchatrain are not included in the
present model, the general trend of the water level predicted by the present model is not
correct when the hydrograph due to Hurricane Katrina is compared with the observed
hydrograph at Little Irish Bayou site from Figure 4.27.
Because the general trends of water levels either are correctly predicted at the 17
th
Street
Canal, the Orleans Avenue Canal, the London Avenue Canal, the IHNC-Lakefront
Airport, the Midlake, and the Pass Manchac-Manchac sites and are reasonably predicted
at the Bayou La Branche, Pass Manchac-Turtle Cove, and the Little Irish Bayou sites by
the present model when the hydrographs due to Hurricane Katrina are compared with the
constructed/observed hydrographs at these sites, it is confident to claim that the present
model for solving the depth-averaged, non-linear shallow water equations (NLSW) is a
reliable numerical model to study the oscillations of semi-enclosed water body induced
by hurricanes even though the present model can not correctly predict the general trends
of the water levels when the hydrographs due to Hurricane Katrina are compared with the
available observed hydrographs at Bayou La Branche, Pass Manchac-Turtle Cove, and
69
Little Irish Bayou sites. Furthermore, the present model will be used in several detailed
studies of the oscillations (storm surges) in Lake Pontchartrain induced by winds
generated through Hurricane Katrina and other simulated hurricanes.
4.5 Applications of Numerical Model
After the validity of the present model for solving the depth-averaged, non-linear shallow
water equations (NLSW) has been affirmed, the present model is applied to study the
wind-induced oscillations in Lake Pontchartrain generated by four (4) different synthetic
hurricanes:
1. Original Hurricane Katrina (Route 1 shown in Figure 4.28).
2. Hurricane Katrina passing above east part of New Orleans, Louisiana (Route 2
shown in Figure 4.28).
3. Hurricane Katrina passing through the regions along the west shore of Lake
Pontchartrain, including Lake Maurepas (Route 3 shown in Figure 4.28).
4. A simulated hurricane traveling the same route as Hurricane Katrina with reduced
forward speeds (Route 1 shown in Figure 4.28).
In order to examine the oscillations in Lake Pontchartrain induced by wind generated
through these hurricanes in detail, including original Hurricane Katrina, two cross
sections (South-North (S-N) and West-East (W-E)) of Lake Pontchartrain are drawn and
70
the reference WSE (η ) is adjusted to zero. The map showing the locations of both cross
sections of Lake Pontchartrain is presented on Figure 4.29. The computed hydrographs
of both S-N and W-E cross sections and the computed contour maps of the entire Lake
Pontchartrain are used to present the oscillation phenomena in Lake Pontchartrain
induced by winds generated through these four (4) hurricanes. The discussions of these
hydrographs and contours maps showing the wind-induced oscillations in Lake
Pontchartrain generated by the present model are presented in the following sub-sections.
Figure 4.28 Map Showing Different Routes of Hurricanes
71
Figure 4.29 Approximate Locations of S-N and W-E cross-sections
4.5.1 Original Hurricane Katrina (Route 1)
The present model is used to study the oscillation in Lake Pontchartrain induced by wind
generated by the Route 1-traveling Hurricane Katrina (see Figure 4.28). The dimensions
of the uniform rectangular control-volumes (CV’s) in a Cartesian grid
are( ) ( ) m m y x 750 , 750 , = ∆ ∆ . The time-step t ∆ is chosen to be 45 seconds. The bathymetry
of Lake Pontchartrain adopted from the Interagency Performance Evaluation Task Force
(IPET) report is used in the numerical simulations (see Figure 4.14). The time-period in
the numerical simulations for the oscillation in Lake Pontchartrain induced by wind
generated by the Route 2-traveling Hurricane Katrina is from 12:00 am UTC
72
(Coordinated Universal Time) August 29, 2005 to 12:00 am UTC August 30, 2005, or
07:00 pm CDT (Central Daylight Time) August 28, 2005 to 07:00 pm CDT August 29,
2005. During this 24-hours time-period, Hurricane Katrina made two landfalls at
Southeast Louisiana and the boarder of Louisiana/Mississippi, respectively, and passed
by the region along the east shore of Lake Pontchartrain (see Figures 4.2 and 4.28).
Hence, the study of the oscillation in Lake Pontchartrain induced by wind generated by
the Route 1-traveling Hurricane Katrina can be concentrated in this 24-hours period. In
order to study the oscillation phenomena in Lake Pontchartrain induced by the Route-1
traveling Hurricane Katrina, the breaches and/or overtopping of floodwalls and levees
along Lake Pontchartrain will not be accommodated into the numerical simulations
performed by the present model for this case; hence, the water can not flow out of the
lake through the entrances of the canals connecting to the lake during the entire 24-hours
period of the numerical simulations for the oscillations of Lake Pontchartrain induced by
the Route-1 traveling Hurricane Katrina.
The wind field inducing the oscillations in Lake Pontchartrain is exclusively caused by
the Route 1-traveling Hurricane Katrina. The numerical typhoon (or hurricane) model,
based on Equation (3.9) through Equation (3.14) in Chapter 3 and developed along with
the present model in this study, is used to generate the pressure and wind fields. The
meteorological data to simulate Hurricane Katrina between 12:00 am UTC August 29,
2005 and 12:00 am UTC August 30, 2005 are adopted from the Interagency Performance
Evaluation Task Force (IPET) report and are listed in Table 4.1. The diameters of the eye
73
of the simulated Hurricane Katrina by the numerical hurricane model are the distances
corresponding to a time interval of a half-hour traveling of the simulated Hurricane
Katrina. The speeds for the simulated Hurricane Katrina derived from the moving path
of Hurricane Katrina between 12:00 am UTC August 29, 2005 and 12:00 am UTC
August 30, 2005 are interpreted from the hourly Latitudes and Longitudes of Hurricane
Katrina recorded in the Interagency Performance Evaluation Task Force (IPET) report.
The computed hydrograph (solid black line) obtained from the present model for the 17
th
Street Canal is presented on Figure 4.30. From Figure 4.30, it is seen that the peak water
surface elevation (WSE, so called water level in the IPET report) computed by the
present model is approximately 3.30 m at the 17
th
Street Canal site. In detail, the water
surface elevations induced by the Route 1-traveling Hurricane Katrina are identical to the
water surface levels induced by the original Hurricane Katrina at the 17
th
Street Canal site
until the 15
th
hour of the numerical simulations (see the solid red line on Figure 4.30).
Due to the absence of the breaches and/or overtopping of floodwalls and levees along
Lake Pontchartrain, the residual water surface elevations for the Route 1-traveling
Hurricane Katrina are much higher than the ones for the original Hurricane Katrina after
the 15
th
hour of the numerical simulations. Hence, this is an evidential proof that the
tremendous amount of water escaping from Lake Pontchartrain through the breaches
and/or overtopping of floodwalls and levees can bring a devastating damage to the
communities surrounding Lake Pontchartrain.
74
Figure 4.30 Computed Hydrograph, 17
th
Street Canal
The computed hydrograph (solid black line) obtained from the present model for the
Orleans Avenue Canal is presented on Figure 4.31. From Figure 4.31, it is seen that the
peak water surface elevation (WSE, so called water level in the IPET report) computed
by the present model is approximately 3.27 m at the Orleans Avenue Canal site. In
detail, the water surface elevations induced by the Route 1-traveling Hurricane Katrina
are identical to the water surface levels induced by the original Hurricane Katrina at the
Orleans Avenue Canal site until the 15
th
hour of the numerical simulations (see the solid
red line on Figure 4.31). Due to the absence of the breaches and/or overtopping of
floodwalls and levees along Lake Pontchartrain, the residual water surface elevations for
the Route 1-traveling Hurricane Katrina are much higher than the ones for the original
75
Hurricane Katrina after the 15
th
hour of the numerical simulations. Hence, this is an
evidential proof that the tremendous amount of water escaping from Lake Pontchartrain
through the breaches and/or overtopping of floodwalls and levees can bring a devastating
damage to the communities surrounding Lake Pontchartrain.
Figure 4.31 Computed Hydrograph, Orleans Avenue Canal
The computed hydrograph (solid black line) obtained from the present model for the
London Avenue Canal is presented on Figure 4.32. From Figure 4.32, it is seen that the
peak water surface elevation (WSE, so called water level in the IPET report) computed
by the present model is approximately 3.30 m at the London Avenue Canal site. In
detail, the water surface elevations induced by the Route 1-traveling Hurricane Katrina
76
are identical to the water surface levels induced by the original Hurricane Katrina at the
London Avenue Canal site until the 15
th
hour of the numerical simulations (see the solid
red line on Figure 4.32). Due to the absence of the breaches and/or overtopping of
floodwalls and levees along Lake Pontchartrain, the residual water surface elevations for
the Route 1-traveling Hurricane Katrina are much higher than the ones for the original
Hurricane Katrina after the 15
th
hour of the numerical simulations. Hence, this is an
evidential proof that the tremendous amount of water escaping from Lake Pontchartrain
through the breaches and/or overtopping of floodwalls and levees can bring a devastating
damage to the communities surrounding Lake Pontchartrain.
Figure 4.32 Computed Hydrograph, London Avenue Canal
77
The computed hydrograph (solid black line) obtained from the present model for the
IHNC-Lakefront Airport is presented on Figure 4.33. From Figure 4.33, it is seen that
the peak water surface elevation (WSE, so called water level in the IPET report)
computed by the present model is approximately 3.30 m at the IHNC-Lakefront Airport
site. In detail, the water surface elevations induced by the Route 1-traveling Hurricane
Katrina are identical to the water surface levels induced by the original Hurricane Katrina
at the IHNC-Lakefront Airport site until the 15
th
hour of the numerical simulations (see
the solid red line on Figure 4.33). Due to the absence of the breaches and/or overtopping
of floodwalls and levees along Lake Pontchartrain, the residual water surface elevations
for the Route 1-traveling Hurricane Katrina are much higher than the ones for the original
Hurricane Katrina after the 15
th
hour of the numerical simulations. Hence, this is an
evidential proof that the tremendous amount of water escaping from Lake Pontchartrain
through the breaches and/or overtopping of floodwalls and levees can bring a devastating
damage to the communities surrounding Lake Pontchartrain.
78
Figure 4.33 Computed Hydrograph, IHNC-Lakefront Airport
The computed hydrograph (solid black line) obtained from the present model for the
Midlake is presented on Figure 4.34. From Figure 4.34, it is seen that the peak water
surface elevation induced by the Route 1-traveling Hurricane Katrina is higher than the
peak water surface level induced by the original Hurricane Katrina at the Midlake site
(see the solid red line on Figure 4.34). Furthermore, the general trend of the rise and fall
of water level induced by the wind generated by the Route 1-traveling Hurricane Katrina
is slightly different from the general trend of the rise and fall of water level induced by
the wind generated by the original Hurricane Katrina. Due to the absence of the breaches
and/or overtopping of floodwalls and levees along Lake Pontchartrain, the residual water
surface elevations for the Route 1-traveling Hurricane Katrina are much higher than the
79
ones for the original Hurricane Katrina after the 15
th
hour of the numerical simulations.
Hence, this is an evidential proof that the tremendous amount of water escaping from
Lake Pontchartrain through the breaches and/or overtopping of floodwalls and levees can
bring a devastating damage to the communities surrounding Lake Pontchartrain.
Figure 4.34 Computed Hydrograph, Midlake
The computed hydrograph (solid black line) obtained from the present model for Bayou
La Branche (named Bayou Labranch in the IPET report) is presented on Figure 4.35. It
can be seen from Figures 4.7 and 4.13 that Bayou La Branche is in the swamp along the
southwest shore of Lake Pontchartrain and the swamps along the entire southwest shore
of Lake Pontchatrain have been assigned into the computational domain for the current
80
numerical simulations performed by the present model. From Figure 4.35, it is seen that
the peak water surface elevation induced by the Route 1-traveling Hurricane Katrina is
equal to the peak water surface level induced by the original Hurricane Katrina at Bayou
La Branche site (see the solid red line on Figure 4.35). Furthermore, the general trend of
the rise and fall of water level induced by the wind generated by the Route 1-traveling
Hurricane Katrina is slightly different from the general trend of the rise and fall of water
level induced by the wind generated by the original Hurricane Katrina. Due to the
absence of the breaches and/or overtopping of floodwalls and levees along Lake
Pontchartrain, the residual water surface elevations for the Route 1-traveling Hurricane
Katrina are much higher than the ones for the original Hurricane Katrina after the 15
th
hour of the numerical simulations. Hence, this is an evidential proof that the tremendous
amount of water escaping from Lake Pontchartrain through the breaches and/or
overtopping of floodwalls and levees can bring a devastating damage to the communities
surrounding Lake Pontchartrain.
81
Figure 4.35 Computed Hydrograph, Bayou La Branche
The computed hydrograph (solid black line) obtained from the present model for Pass
Manchac-Turtle Cove is presented on Figure 4.36. From Figures 4.7 and 4.13, it can be
seen that Pass Manchac is a the narrow strip of water connecting Lake Pontchartrain and
Lake Maurepas and the entire Pass Manchac is included in the computational domain
used in the current numerical simulations performed by the present model. From Figure
4.36, it is seen that the peak water surface elevation induced by the Route 1-traveling
Hurricane Katrina is higher than the peak water surface level induced by the original
Hurricane Katrina at Pass Manchac-Turtle Cove site (see the solid red line on Figure
4.36). Furthermore, the general trend of the rise and fall of water level induced by the
wind generated by the Route 1-traveling Hurricane Katrina is slightly different from the
82
general trend of the rise and fall of water level induced by the wind generated by the
original Hurricane Katrina. Due to the absence of the breaches and/or overtopping of
floodwalls and levees along Lake Pontchartrain, the residual water surface elevations for
the Route 1-traveling Hurricane Katrina are much higher than the ones for the original
Hurricane Katrina after the 15
th
hour of the numerical simulations. Hence, this is an
evidential proof that the tremendous amount of water escaping from Lake Pontchartrain
through the breaches and/or overtopping of floodwalls and levees can bring a devastating
damage to the communities surrounding Lake Pontchartrain.
Figure 4.36 Computed Hydrograph, Pass Manchac-Turtle Cove
83
The computed hydrograph (solid black line) obtained from the present model for Little
Irish Bayou is presented on Figure 4.37. From Figure 4.37, it is seen that the peak water
surface elevation induced by the Route 1-traveling Hurricane Katrina is slightly higher
than the peak water surface level induced by the original Hurricane Katrina at Little Irish
Bayou site (see the solid red line on Figure 4.37). Furthermore, the general trend of the
rise and fall of water level induced by the wind generated by the Route 1-traveling
Hurricane Katrina is slightly different from the general trend of the rise and fall of water
level induced by the wind generated by the original Hurricane Katrina. Due to the
absence of the breaches and/or overtopping of floodwalls and levees along Lake
Pontchartrain, the residual water surface elevations for the Route 1-traveling Hurricane
Katrina are much higher than the ones for the original Hurricane Katrina after the 15
th
hour of the numerical simulations. Hence, this is an evidential proof that the tremendous
amount of water escaping from Lake Pontchartrain through the breaches and/or
overtopping of floodwalls and levees can bring a devastating damage to the communities
surrounding Lake Pontchartrain.
84
Figure 4.37 Computed Hydrograph, Little Irish Bayou
The computed hydrographs of the water surface elevation (WSE) showing on S-N and
W-E cross-sections of Lake Pontchartrain induced by the wind generated through the
Route 1-traveling Hurricane Katrina are presented on Figures 4.38 and 4.39, respectively.
It is seen from Figures 4.38 and 4.39 that the wind-induced oscillations in Lake
Pontchartrain are the evident phenomena as Hurricane Katrina progressed over the
Southeast Louisiana region (Route 1 shown in Figure 4.28). In the following paragraphs,
the hourly contour maps of the water surface elevation (WSE) for the entire Lake
Pontchartrain, as Hurricane Katrina progressed over the Southeast Louisiana region
(Route 1 shown in Figure 4.28, which is the exact route of Hurricane Katrina), are used to
85
investigate the oscillations of semi-enclosed water body induced by hurricanes under
specific routes.
The hourly contour maps of the computed water surface elevation (WSE) for the entire
Lake Pontchartrain induced by the wind generated through the original Hurricane Katrina
are presented from Figures 4.40 to Figures 4.64. The time-frame of these contour maps is
from 12:00 am UTC August 29, 2005 to 12:00 am UTC August 30, 2005. It is assigned
that 0 t = is at 11:59:15 pm UTC August 28, 2005 and consequently the reference WSE
at 0 t = is zero. Therefore, the oscillation phenomenon is not evident throughout entire
Lake Pontchartrain at the starting moment of the numerical simulation (12:00 am August
29, 2005), as it is seen from Figure 4.40. As it is seen from Figures 4.2 and 4.28, the
original Hurricane Katrina did not make its landfall until 6:10 am CDT (11:10 am UTC)
August 29 at Southeast Louisiana and the Route 1 is the exact route of the original
Hurricane Katrina; besides, the oscillation induced by tides from Gulf of Mexico into
Lake Pontchartrain is not influential in this study, this is a reasonable assumption that the
oscillations in Lake Pontchartrain induced by wind generated by the Route 1-traveling
Hurricane Katrina can be focused on the 24-hours period between 12:00 am UTC August
29, 2005 and 12:00 am UTC August 30, 2005.
86
Figure 4.38 Hydrographs of the S-N cross-section
Figure 4.39 Hydrographs of the W-E cross-section
87
Figure 4.40 Contours of WSE at 12:00 am (UTC) August 29, 2005
Figure 4.41 Contours of WSE at 01:00 am (UTC) August 29, 2005
88
Figure 4.42 Contours of WSE at 02:00 am (UTC) August 29, 2005
Figure 4.43 Contours of WSE at 03:00 am (UTC) August 29, 2005
89
Figure 4.44 Contours of WSE at 04:00 am (UTC) August 29, 2005
Figure 4.45 Contours of WSE at 05:00 am (UTC) August 29, 2005
90
Figure 4.46 Contours of WSE at 06:00 am (UTC) August 29, 2005
Figure 4.47 Contours of WSE at 07:00 am (UTC) August 29, 2005
91
Figure 4.48 Contours of WSE at 08:00 am (UTC) August 29, 2005
Figure 4.49 Contours of WSE at 09:00 am (UTC) August 29, 2005
92
Figure 4.50 Contours of WSE at 10:00 am (UTC) August 29, 2005
Figure 4.51 Contours of WSE at 11:00 am (UTC) August 29, 2005
93
Figure 4.52 Contours of WSE at 12:00 pm (UTC) August 29, 2005
Figure 4.53 Contours of WSE at 01:00 pm (UTC) August 29, 2005
94
Figure 4.54 Contours of WSE at 02:00 pm (UTC) August 29, 2005
Figure 4.55 Contours of WSE at 03:00 pm (UTC) August 29, 2005
95
Figure 4.56 Contours of WSE at 04:00 pm (UTC) August 29, 2005
Figure 4.57 Contours of WSE at 05:00 pm (UTC) August 29, 2005
96
Figure 4.58 Contours of WSE at 06:00 pm (UTC) August 29, 2005
Figure 4.59 Contours of WSE at 07:00 pm (UTC) August 29, 2005
97
Figure 4.60 Contours of WSE at 08:00 pm (UTC) August 29, 2005
Figure 4.61 Contours of WSE at 09:00 pm (UTC) August 29, 2005
98
Figure 4.62 Contours of WSE at 10:00 pm (UTC) August 29, 2005
Figure 4.63 Contours of WSE at 11:00 pm (UTC) August 29, 2005
99
Figure 4.64 Contours of WSE at 12:00 am (UTC) August 30, 2005
It can be seen from Figures 4.41 to 4.46 that the oscillation in Lake Pontchartrain is built
up as Hurricane Katrina approaches to Southeast Louisiana and it becomes more obvious
as time goes by. It is very evident that the direction of node line ( 0 = η ) in the lake is in
the North-South orientation. It is seen that the water in the east part of the lake is driven
by the wind to the west part of the lake during the first 6-hour period, as we examine the
temporal variations of the contours of WSE from 12:00 to 06:00 am UTC August 29,
2005. The strength of Hurricane Katrina, according to the IPET report, is gradually
reducing from Category 4 to 3 in Saffir-Simpson Scale within this 6-hours period.
100
As the hurricane approaches Southeast Louisiana and makes its first landfall at
approximately 11:10 am UTC (6:10 am Local Time) August 29, the magnitude of
oscillation in the lake gradually increases between 07:00 am UTC and 12:00 pm UTC
August 29, 2005. During this 6-hours period, the direction of node line ( 0 = η ) in the
lake slowly changes from the North-South orientation to the Northwest-Southeast
orientation since the direction of the dominant wind alters as Hurricane Katrina
approaches to Lake Pontchartrain while its strength remains Category 3. We can see
these phenomena after examining the temporal variations of the contours of WSE from
Figures 4.47 to 4.52.
From 12:00 pm UTC to 03:00 pm UTC August 29, Hurricane Katrina passes nearby the
east shore of Lake Pontchartrain. Thus, this close-encounter between the hurricane and
the lake causes significant oscillations in Lake Pontchartrain as we compare the
oscillations happened in the lake during the previous 12 hours. It is seen from Figures
4.53 to 4.55 that the direction of node line ( 0 = η ) in the lake changes from the
Northwest-Southeast orientation to the West-East orientation as the direction of the
dominant wind rapidly alters during this 3-hours period. Meanwhile, the magnitude of
oscillation (the height of WSE) becomes higher than the previous 6 hours, and the
oscillation along the south shore of Lake Pontchartrain reaches the highest magnitude
between 02:30 and 03:00 pm UTC (or 09:30 and 10:00 am Local Time), as we have
already seen from Figures 4.30 to 4.33. Within this 3-hours period, Hurricane Katrina
makes its second landfall at approximately 02:45 pm UTC (09:45 am Local Time) near
101
Louisiana/Mississippi border (as it is seen from Route 1 shown in Figure 4.28) and its
strength still remains Category 3.
During the next 3-hours period (from 03:00 to 06:00 pm UTC August 29), the Hurricane
Katrina continuously moves inland with a nearly north direction and its strength reduces
from Category 3 to 2. Meanwhile, the direction of node line ( 0 = η ) rapidly turns from
the West-East orientation to the South-North orientation as the direction of the dominant
wind alters
o
90 in a counterclockwise pattern even though the wind generated by the
hurricane gets weaker during this 3-hours time-period. Because the surge propagates into
Lake Pontchartrain from the Gulf of Mexico via Lake Borgne (see Figure 4.3), an
enormous amount of water flows into Lake Pontchartrain and the magnitude of
oscillation (the height of WSE) in Lake Pontchartrain significantly increases even though
the hurricane leaves the northeast regions of the lake. Furthermore, the node line ( 0 = η )
disappears and the WSE in the entire lake is greater than the reference WSE ( 0 = η ) from
04:00 pm, as it is seen from Figure 4.56. We can find these evidences from a thorough
study of the temporal variations of the contours of WSE from Figures 4.56 to 4.58.
In the final 6-hours period (from 07:00 pm UTC August 29 to 12:00 am UTC August 30,
2005), the strength of Hurricane Katrina continuously reduces from Category 2 to 1 and
finally Hurricane Katrina becomes a tropical storm as it moves inwardly into the
northeastern region of the United States of America. Although the direction of dominant
102
wind keeps turning counterclockwise during this 6-hours period, the wind generated by
the hurricane is drastically weaker than it was in the previous 18-hours period. Since the
hurricane moves far away from the lake, the magnitude of oscillation in Lake
Pontchartrain gradually reduces and is smaller than it was in the previous 6-hour period.
Besides, the major sloshing motion is moving toward the east within this 6-hours period.
The WSE in the lake does not significantly recede since there is not enough wind stress to
drive out the water from Lake Pontchartrain to Lake Borgne and other surrounding water
bodies; hence, the WSE in the entire lake is greater than the reference WSE ( 0 = η ) in
this 6-hours period. Meanwhile, there is a significant drawdown in the east portion of
Lake Pontchartrain at the finale of the numerical simulation (12:00 am August 30, 2005)
as it is seen from Figure 4.64. We can obtain these discoveries by examining the
temporal variations of WSE from Figures 4.59 to 4.64. Furthermore, the significant
findings drawn from these hourly contour maps (from Figures 4.40 to 4.64) are
summarized in the following paragraphs.
The Route 1-traveling Hurricane Katrina moves in a nearly north direction and passes
through the regions close to the east shore of Lake Pontchartrain (Route 1 shown in
Figure 4.28) between 12:00 am and 06:00 pm UTC August 29, 2005 corresponding to the
first 18-hours of the numerical simulations made by the present model. The closest
encounter between Hurricane Katrina and Lake Pontchartrain takes place between 12:00
and 06:00 pm UTC (or 7:00 am and 1:00 pm Local Time) August 29, 2005 (see Figure
103
4.2). During this 6-hours period, there are three significant factors of Hurricane Katrina
needed to be reviewed:
1. The hurricane remains Category 3 intensity of Saffir-Simpson Scale until 03:00
pm UTC (10:00 am Local Time), after which the strength of the hurricane
gradually reduces to Category 2.
2. The hurricane is moving in a nearly north direction with an approximate speed of
27 to 29 km/hr.
3. The distance between the eye of the hurricane and the east shore of the lake is
approximately 12 km.
Because of these three unique characteristics of the interaction between the hurricane and
the lake, the sloshing motion of the lake water surface changes in a counterclockwise
pattern in the lake as the hurricane itself rotates in the counterclockwise character. In
detail, the dominant sloshing motion at Lake Pontchartrain turns from the southwest to
the east within this 6-hours period. During this 6-hours, the highest amplitude of
oscillation (maximum WSE) along the south shore of the lake happens around 03:00 pm
UTC (10:00 am Local Time) with a magnitude of 3.27 m to 3.30 m predicted by the
present model while the highest measured water level associated with this 6-hours period
is within the range of 10.8 ft to 12.0 ft (or 3.29 m to 3.66 m) along the south shore of
Lake Pontchartrain.
104
Furthermore, the moving direction of the storm surge changes from the west direction to
the east direction within the first 16-hours period (12:00 am to 04:00 pm UTC August 29,
2005) of the numerical simulations (see Figures 4.40 to 56); in other words, the sloshing
motion changes
o
180 in 16 hours. Therefore, the oscillation (rise and fall of water level)
in a semi-enclosed lake induced by a hurricane will be moving around the lake in a
counterclockwise-turning pattern. While a hurricane circulates counterclockwise and the
direction of the accompanying wind generated by the hurricane turns in a
counterclockwise pattern, the magnitude of oscillation thoroughly depends on the
strength (wind speed) and the duration (length in time) of the wind to a specific direction.
In other words, the magnitude of the oscillation (height of rise and fall) associated with
the moving direction will be different at each specific location around the lake.
4.5.2 Hurricane Katrina Traveling Along Route 2
The present model is used to study the oscillation in Lake Pontchartrain induced by wind
generated by the Route 2-traveling Hurricane Katrina (see Figure 4.28). The dimensions
of the uniform rectangular control-volumes (CV’s) in a Cartesian grid
are( ) ( ) m m y x 750 , 750 , = ∆ ∆ . The time-step t ∆ is chosen to be 45 seconds. The bathymetry
of Lake Pontchartrain adopted from the Interagency Performance Evaluation Task Force
(IPET) report is used in the numerical simulations (see Figure 4.14). The time-period in
the numerical simulations for the oscillation in Lake Pontchartrain induced by wind
105
generated by the Route 2-traveling Hurricane Katrina is from 12:00 am UTC
(Coordinated Universal Time) August 29, 2005 to 12:00 am UTC August 30, 2005, or
07:00 pm CDT (Central Daylight Time) August 28, 2005 to 07:00 pm CDT August 29,
2005. During this 24-hours time-period, Hurricane Katrina will make its landfall at
Southeast Louisiana and will pass through the east part of New Orleans, Louisiana and
above the central and east parts of Lake Pontchartrain (see Figures 4.2 and 4.28). Hence,
the study of the oscillation in Lake Pontchartrain induced by wind generated by the Route
2-traveling Hurricane Katrina can be concentrated in this 24-hours period. In order to
study the oscillation phenomena in Lake Pontchartrain induced by the Route-2 traveling
Hurricane Katrina, the breaches and/or overtopping of floodwalls and levees along Lake
Pontchartrain will not be accommodated into the numerical simulations performed by the
present model for this case; hence, the water can not flow out of the lake through the
entrances of the canals connecting to the lake during the entire 24-hours period of the
numerical simulations for the oscillations of Lake Pontchartrain induced by the Route-2
traveling Hurricane Katrina.
The wind field inducing the oscillations in Lake Pontchartrain is exclusively caused by
the Route 2-traveling Hurricane Katrina. The numerical typhoon (or hurricane) model,
based on Equation (3.9) through Equation (3.14) in Chapter 3 and developed along with
the present model in this study, is used to generate the pressure and wind fields. The
meteorological data to simulate Hurricane Katrina between 12:00 am UTC August 29,
2005 and 12:00 am UTC August 30, 2005 are adopted from the Interagency Performance
106
Evaluation Task Force (IPET) report and are listed in Table 4.1. The diameters of the eye
of the simulated Hurricane Katrina by the numerical hurricane model are the distances
corresponding to a time interval of a half-hour traveling of the simulated Hurricane
Katrina. The speeds for the simulated Hurricane Katrina derived from the moving path
of Hurricane Katrina between 12:00 am UTC August 29, 2005 and 12:00 am UTC
August 30, 2005 are interpreted from the hourly Latitudes and Longitudes of Hurricane
Katrina recorded in the Interagency Performance Evaluation Task Force (IPET) report.
The computed hydrograph (solid black line) obtained from the present model for the 17
th
Street Canal is presented on Figure 4.65. From Figure 4.65, it is seen that the peak water
surface elevation (WSE, so called water level in the IPET report) computed by the
present model is approximately 3.86 m at the 17
th
Street Canal site. Besides, it is seen
that the peak water surface elevation induced by the Route 2-traveling Hurricane Katrina
is much higher than the peak water surface level induced by the Route 1-traveling
Hurricane Katrina at the 17
th
Street Canal site (3.86 m versus 3.30 m) after comparing the
computed hydrograph made under the wind generated by the Route 2-traveling Hurricane
Katrina with the one made under the wind generated by the Route 1-traveling Hurricane
Katrina (see the solid red line on Figure 4.65). Therefore, it can be claimed that this
significant difference in water surface elevation is caused by a hurricane passing over
Lake Pontchartrain with another route although the strength (pressure and wind speed) of
the simulated Hurricane Katrina is identical to the original one.
107
Figure 4.65 Computed Hydrograph, 17
th
Street Canal
The computed hydrograph (solid black line) obtained from the present model for the
Orleans Avenue Canal is presented on Figure 4.66. From Figure 4.66, it is seen that the
peak water surface elevation (WSE, so called water level in the IPET report) computed
by the present model is approximately 3.53 m at the Orleans Avenue Canal site. Besides,
it is seen that the peak water surface elevation induced by the Route 2-traveling
Hurricane Katrina is much higher than the peak water surface level induced by the Route
1-traveling Hurricane Katrina at the Orleans Avenue Canal site (3.53 m versus 3.27 m)
after comparing the computed hydrograph made under the wind generated by the Route
2-traveling Hurricane Katrina with the one made under the wind generated by the Route
1-traveling Hurricane Katrina (see the solid red line on Figure 4.66). Therefore, it can be
108
claimed that hurricane passing over Lake Pontchartrain with another route can cause a
significant difference in water surface elevation although the strength (pressure and wind
speed) of the simulated Hurricane Katrina is identical to the original one.
Figure 4.66 Computed Hydrograph, Orleans Avenue Canal
The computed hydrograph (solid black line) obtained from the present model for the
London Avenue Canal is presented on Figure 4.67. From Figure 4.67, it is seen that the
peak water surface elevation (WSE, so called water level in the IPET report) computed
by the present model is approximately 3.53 m at the London Avenue Canal site. Besides,
it is seen that the peak water surface elevation induced by the Route 2-traveling
Hurricane Katrina is much higher than the peak water surface level induced by the Route
109
1-traveling Hurricane Katrina at the London Avenue Canal site (3.53 m versus 3.30 m)
after comparing the computed hydrograph made under the wind generated by the Route
2-traveling Hurricane Katrina with the one made under the wind generated by the Route
1-traveling Hurricane Katrina (see the solid red line on Figure 4.67). Therefore, it can be
claimed that this evident difference in water surface elevation is caused by a hurricane
passing over Lake Pontchartrain with another route although the strength (pressure and
wind speed) of the simulated Hurricane Katrina is identical to the original one.
Figure 4.67 Computed Hydrograph, London Avenue Canal
The computed hydrograph (solid black line) obtained from the present model for the
IHNC-Lakefront Airport is presented on Figure 4.68. From Figure 4.68, it is seen that
110
the peak water surface elevation (WSE, so called water level in the IPET report)
computed by the present model is approximately 3.60 m at the IHNC-Lakefront Airport
site. Besides, it is seen that the peak water surface elevation induced by the Route 2-
traveling Hurricane Katrina is much higher than the peak water surface level induced by
the Route 1-traveling Hurricane Katrina at the IHNC-Lakefront Airport site (3.60 m
versus 3.30 m) after comparing the computed hydrograph made under the wind generated
by the Route 2-traveling Hurricane Katrina with the one made under the wind generated
by the Route 1-traveling Hurricane Katrina (see the solid red line on Figure 4.68).
Therefore, it can be claimed that hurricane passing over Lake Pontchartrain with another
route can cause an evident difference in water surface elevation although the strength
(pressure and wind speed) of the simulated Hurricane Katrina is identical to the original
one.
111
Figure 4.68 Computed Hydrograph, IHNC-Lakefront Airport
The computed hydrograph (solid black line) obtained from the present model for the
Midlake is presented on Figure 4.69. From Figure 4.69, it is seen that the peak water
surface elevation induced by the Route 2-traveling Hurricane Katrina is much higher than
the peak water surface level induced by the Route 1-traveling Hurricane Katrina at the
Midlake site after comparing the computed hydrograph made under the wind generated
by the Route 2-traveling Hurricane Katrina with the one made under the wind generated
by the Route 1-traveling Hurricane Katrina (see the solid red line on Figure 4.69).
Furthermore, the general trend of the rise and fall of water level induced by the wind
generated by the Route 2-traveling Hurricane Katrina is slightly different from the
general trend of the rise and fall of water level induced by the wind generated by the
112
Route 1-traveling Hurricane Katrina. Therefore, it can be claimed that these evident
differences in the water surface elevations are caused by a hurricane passing over Lake
Pontchartrain with another route although the strength (pressure and wind speed) of the
simulated Hurricane Katrina is identical to the original one.
Figure 4.69 Computed Hydrograph, Midlake
The computed hydrograph (solid black line) obtained from the present model for Bayou
La Branche (named Bayou Labranch in the IPET report) is presented on Figure 4.70. It
can be seen from Figures 4.7 and 4.13 that Bayou La Branche is in the swamp along the
southwest shore of Lake Pontchartrain and the swamps along the entire southwest shore
of Lake Pontchatrain have been assigned into the computational domain for the current
113
numerical simulations performed by the present model. From Figure 4.70, it is seen that
the peak water surface elevation induced by the Route 2-traveling Hurricane Katrina is
much higher than the peak water surface level induced by the original Hurricane Katrina
at Bayou La Branche site after comparing the computed hydrograph made under the wind
generated by the Route 2-traveling Hurricane Katrina with the one made under the wind
generated by the Route 1-traveling Hurricane Katrina (see the solid red line on Figure
4.70). Besides, the general trends of the rise and fall of water levels on both computed
hydrographs (solid black and solid red lines on Figure 4.70) made by the present model
are almost identical although the highest water surface elevations induced by the winds
generated by two hurricanes (Route 2-traveling Katrina and Route 1-traveling Katrina)
are significantly different at Bayou La Branche site. Therefore, it can be claimed that this
evident difference in the water surface elevation is caused by a hurricane passing over
Lake Pontchartrain with another route although the strength (pressure and wind speed) of
the simulated Hurricane Katrina is identical to the original one.
114
Figure 4.70 Computed Hydrograph, Bayou La Branche
The computed hydrograph (solid black line) obtained from the present model for Pass
Manchac-Turtle Cove is presented on Figure 4.71. From Figures 4.7 and 4.13, it can be
seen that Pass Manchac is a the narrow strip of water connecting Lake Pontchartrain and
Lake Maurepas and the entire Pass Manchac is included in the computational domain
used in the current numerical simulations performed by the present model. From Figure
4.71, it is seen that the peak water surface elevation induced by the Route 2-traveling
Hurricane Katrina is slightly higher than the peak water surface level induced by the
original Hurricane Katrina at Pass Manchac-Turtle Cove site after comparing the
computed hydrograph made under the wind generated by the Route 2-traveling Hurricane
Katrina with the one made under the wind generated by the Route 1-traveling Hurricane
115
Katrina (see the solid red line on Figure 4.71). Besides, the general trends of the rise and
fall of water levels on both computed hydrographs (solid black and solid red lines on
Figure 4.71) made by the present model are almost identical although the highest water
surface elevations induced by the winds generated by two hurricanes are different at Pass
Manchac-Turtle Cove site. Therefore, it can be claimed that this evident difference in the
water surface elevation is caused by a hurricane passing over Lake Pontchartrain-Turtle
Cove with another route although the strength (pressure and wind speed) of the simulated
Hurricane Katrina is identical to the original one.
Figure 4.71 Computed Hydrograph, Pass Manchac-Turtle Cove
116
The computed hydrograph (solid black line) obtained from the present model for Little
Irish Bayou is presented on Figure 4.72. From Figure 4.72, it is seen that the peak water
surface elevation induced by the Route 2-traveling Hurricane Katrina is much higher than
the peak water surface level induced by the Route 1-traveling Hurricane Katrina at Little
Irish Bayou site after comparing the computed hydrograph made under the wind
generated by the Route 2-traveling Hurricane Katrina with the one made under the wind
generated by the Route 1-traveling Hurricane Katrina (see the solid red line on Figure
4.72). Besides, the general trends of the rise and fall of water levels on both computed
hydrographs (solid black and solid red lines on Figure 4.72) made by the present model
are almost identical although the highest water surface elevations induced by the winds
generated by two hurricanes are significantly different at Little Irish Bayou site.
Therefore, it can be claimed that this evident difference in the water surface elevation is
caused by a hurricane passing over Lake Pontchartrain with another route although the
strength (pressure and wind speed) of the simulated Hurricane Katrina is identical to the
original one.
117
Figure 4.72 Computed Hydrograph, Little Irish Bayou
The computed hydrographs of the water surface elevation (WSE) showing on S-N and
W-E cross-sections of Lake Pontchartrain induced by the wind generated through the
Route 2-traveling Hurricane Katrina (see Figure 4.28) are presented on Figures 4.73 and
4.74, respectively. It is seen from Figures 4.73 and 4.74 that the wind-induced
oscillations in Lake Pontchartrain are the evident phenomena as Hurricane Katrina
progressed over the east part of New Orleans, Louisiana (Route 2 shown in Figure 4.28).
In the following paragraphs, the hourly contour maps of the water surface elevation
(WSE) for the entire Lake Pontchartrain, as Hurricane Katrina progressed over the east
part of New Orleans, Louisiana (Route 2 shown in Figure 4.28), ware used to investigate
the oscillations of semi-enclosed water body induced by hurricanes under specific routes.
118
Figure 4.73 Hydrographs of the S-N cross-section
Figure 4.74 Hydrographs of the W-E cross-section
119
The hourly contour maps of the computed water surface elevation (WSE) for the entire
Lake Pontchartrain induced by the wind generated through the Route 2-traveling
Hurricane Katrina are presented from Figures 4.75 to Figures 4.99. The time-frame of
these contour maps is from 12:00 am UTC August 29, 2005 to 12:00 am UTC August 30,
2005. It is assigned that 0 t = is at 11:59:15 pm UTC August 28, 2005 and consequently
the reference WSE at 0 t = is zero. Therefore, the oscillation phenomenon is not evident
throughout entire Lake Pontchartrain at the starting moment of the numerical simulation
(12:00 am August 29, 2005), as it is seen from Figure 4.75. As it is seen from Figures 4.2
and 4.28, the original Hurricane Katrina did not make its landfall until 6:10 am CDT
(11:10 am UTC) August 29 at Southeast Louisiana and the distance between the Route 1
and Route 2 is approximately 36 km; besides, the oscillation induced by tides from Gulf
of Mexico into Lake Pontchartrain is not influential in this study, this is a reasonable
assumption that the oscillations in Lake Pontchartrain induced by wind generated by the
Route 2-traveling Hurricane Katrina can be focused on the 24-hours period between
12:00 am UTC August 29, 2005 and 12:00 am UTC August 30, 2005.
120
Figure 4.75 Contours of WSE at 12:00 am (UTC) August 29, 2005
Figure 4.76 Contours of WSE at 01:00 am (UTC) August 29, 2005
121
Figure 4.77 Contours of WSE at 02:00 am (UTC) August 29, 2005
Figure 4.78 Contours of WSE at 03:00 am (UTC) August 29, 2005
122
Figure 4.79 Contours of WSE at 04:00 am (UTC) August 29, 2005
Figure 4.80 Contours of WSE at 05:00 am (UTC) August 29, 2005
123
Figure 4.81 Contours of WSE at 06:00 am (UTC) August 29, 2005
Figure 4.82 Contours of WSE at 07:00 am (UTC) August 29, 2005
124
Figure 4.83 Contours of WSE at 08:00 am (UTC) August 29, 2005
Figure 4.84 Contours of WSE at 09:00 am (UTC) August 29, 2005
125
Figure 4.85 Contours of WSE at 10:00 am (UTC) August 29, 2005
Figure 4.86 Contours of WSE at 11:00 am (UTC) August 29, 2005
126
Figure 4.87 Contours of WSE at 12:00 pm (UTC) August 29, 2005
Figure 4.88 Contours of WSE at 01:00 pm (UTC) August 29, 2005
127
Figure 4.89 Contours of WSE at 02:00 pm (UTC) August 29, 2005
Figure 4.90 Contours of WSE at 03:00 pm (UTC) August 29, 2005
128
Figure 4.91 Contours of WSE at 04:00 pm (UTC) August 29, 2005
Figure 4.92 Contours of WSE at 05:00 pm (UTC) August 29, 2005
129
Figure 4.93 Contours of WSE at 06:00 pm (UTC) August 29, 2005
Figure 4.94 Contours of WSE at 07:00 pm (UTC) August 29, 2005
130
Figure 4.95 Contours of WSE at 08:00 pm (UTC) August 29, 2005
Figure 4.96 Contours of WSE at 09:00 pm (UTC) August 29, 2005
131
Figure 4.97 Contours of WSE at 10:00 pm (UTC) August 29, 2005
Figure 4.98 Contours of WSE at 11:00 pm (UTC) August 29, 2005
132
Figure 4.99 Contours of WSE at 12:00 am (UTC) August 30, 2005
It can be seen from Figures 4.76 to 4.84 that the oscillation in Lake Pontchartrain is built
up as Hurricane Katrina approaches to Southeast Louisiana and it becomes more obvious
as time goes by. It is very evident that the direction of node line ( 0 = η ) in the lake is in
the North-South orientation. Besides, it is possible that the Route 2-traveling Hurricane
Katrina makes its landfall at Southeast Louisiana around 11:00 am UTC (6:00 am Local
Time) August 29 since the distance between Route 1 and Route 2 is about only 36 km
(see Figures 4.2 and 4.28). It is seen that the water in the east part of the lake is driven by
the wind to the west part of the lake during the first 9-hour period, as we examine the
temporal variations of the contours of WSE from 12:00 to 09:00 am UTC August 29,
133
2005. The strength of Hurricane Katrina, according to the IPET report, is gradually
reducing from Category 4 to 3 in Saffir-Simpson Scale within this 9-hours period.
As the Route 2-traveling Hurricane Katrina approaches Southeast Louisiana, the
magnitude of oscillation in the lake gradually increases between 09:00 am UTC and
12:00 pm UTC August 29, 2005. During this 3-hours period, the direction of node line
( 0 = η ) in the lake changes from the North-South orientation to the slightly Northwest-
Southeast orientation since the direction of the dominant wind alters as Hurricane Katrina
approaches to Lake Pontchartrain while its strength remains Category 3. We can see
these phenomena after examining the temporal variations of the contours of WSE from
Figures 4.85 to 4.87.
From 12:00 pm UTC to 03:00 pm UTC August 29, the Route 2-traveling Hurricane
Katrina passes over the east part of New Orleans, Louisiana, and the south-central part of
Lake Pontchartrain. Thus, this close-encounter between the hurricane and the lake causes
significant oscillations in Lake Pontchartrain as we compare the oscillations happened in
the lake during the previous 12 hours. It is seen from Figures 4.88 to 4.90 that the
direction of node line ( 0 = η ) in the lake changes from the slightly Northwest-Southeast
orientation to the nearly West-East orientation as the direction of the dominant wind
rapidly alters during this 3-hours period. Meanwhile, the magnitude of oscillation (the
height of WSE) becomes higher than the previous 3 hours, and the oscillation along the
southeast and south shores of Lake Pontchartrain reaches the highest magnitude between
02:30 and 03:00 pm UTC (or 09:30 and 10:00 am Local Time), as we have already seen
134
from Figures 4.65 to 4.88. Within this 3-hours period, the strength of the Route 2-
traveling Hurricane Katrina still remains Category 3.
During the next 3-hours period (from 03:00 to 06:00 pm UTC August 29), the Route 2-
traveling Hurricane Katrina continuously crosses over Lake Pontchartrain and moves
inland with a nearly north direction while its strength reduces from Category 3 to 2.
Meanwhile, the direction of node line ( 0 = η ) rapidly turns from the nearly West-East
orientation to the nearly South-North orientation as the direction of the dominant wind
alters
o
90 in a counterclockwise pattern even though the wind generated by the hurricane
gets weaker during this 3-hours time-period. Because the surge propagates into Lake
Pontchartrain from the Gulf of Mexico via Lake Borgne (see Figure 4.3), a huge amount
of water flows into Lake Pontchartrain and the magnitude of oscillation (the height of
WSE) in Lake Pontchartrain evidently increases even though the hurricane leaves the
central and northeast regions of the lake. Furthermore, the node line ( 0 = η ) disappears
and the WSE in the entire lake is greater than the reference WSE ( 0 = η ) from 06:00 pm,
as it is seen from Figure 4.93. We can find these evidences from a thorough study of the
temporal variations of the contours of WSE from Figures 4.91 to 4.93.
In the final 6-hours period (from 07:00 pm UTC August 29 to 12:00 am UTC August 30,
2005), the strength of the Route 2-traveling Hurricane Katrina continuously reduces from
Category 2 to 1; furthermore, the Route 2-traveling Hurricane Katrina becomes a tropical
135
storm as it moves inwardly into the northeastern region of the United States of America
as the original Hurricane Katrina moves inwardly (see Figures 4.2 and 4.28). Although
the direction of dominant wind keeps turning counterclockwise during this 6-hours
period, the wind generated by the hurricane is drastically weaker than it was in the
previous 18-hours period. Since the hurricane moves far away from the lake, the
magnitude of oscillation in Lake Pontchartrain gradually reduces and is smaller than it
was in the previous 6-hour period. Besides, the major sloshing motion is moving toward
the east within this 6-hours period. The WSE in the lake does not significantly recede
since there is not enough wind stress to drive out the water from Lake Pontchartrain to
Lake Borgne and other surrounding water bodies (for example, Lake Maurepas); hence,
the WSE in the entire lake is greater than the reference WSE ( 0 = η ) in this 6-hours
period. Meanwhile, there is a significant drawdown in the east portion of Lake
Pontchartrain at the finale of the numerical simulation (10:00 pm August 29 to 12:00 am
August 30, 2005) as it is seen from Figures 4.84 to 4.86. We can obtain these discoveries
by examining the temporal variations of WSE from Figures 4.94 to 4.99. Furthermore,
the significant findings drawn from these hourly contour maps (from Figures 4.75 to
4.99) are summarized in the following paragraphs.
The Route 2-traveling Hurricane Katrina moves in a nearly north direction and passes
over the east part of New Orleans, Louisiana and the central and east parts of Lake
Pontchartrain between 12:00 am and 06:00 pm UTC August 29, 2005 corresponding to
the first 18-hours of the numerical simulations made by the present model. The closest
136
encounter between Hurricane Katrina and Lake Pontchartrain takes place between 12:00
and 06:00 pm UTC (or 7:00 am and 1:00 pm Local Time) August 29, 2005 (see Figure
4.2). During this 6-hours period, there are three significant factors of Hurricane Katrina
needed to be reviewed:
1. The hurricane remains Category 3 intensity of Saffir-Simpson Scale until 03:00
pm UTC (10:00 am Local Time), after which the strength of the hurricane
gradually reduces to Category 2.
2. The hurricane is moving in a nearly north direction with an approximate speed of
27 to 29 km/hr.
3. The eye of the Route 2-traveling Hurricane Katrina passes through the south and
southwest shores of Lake Pontchartrain.
Because of these three unique characteristics of the interaction between the hurricane and
the lake, the sloshing motion of the lake water surface changes in a counterclockwise
pattern in the lake as the hurricane itself rotates in the counterclockwise character. In
detail, the dominant sloshing motion at Lake Pontchartrain turns from the slightly
southwest to the east within this 6-hours period. During this 6-hours, the highest
amplitude of oscillation (maximum WSE) along the south shore of the lake happens
between 02:30 and 03:00 pm UTC (between 09:30 and 10:00 am Local Time) with a
magnitude of 3.53 m to 3.86 m predicted by the newly developed finite-volume method
(FVM) model.
137
Furthermore, the moving direction of the storm surge changes from the west direction to
the east direction within the first 16-hours period (12:00 am to 04:00 pm UTC August 29,
2005) of the numerical simulations (see Figures 4.75 to 91); in other words, the sloshing
motion changes
o
180 in 16 hours. Therefore, the oscillation (rise and fall of water level)
in a semi-enclosed lake induced by a hurricane will be moving around the lake in a
counterclockwise-turning pattern whenever a hurricane either passes through the regions
along the east shore or pass over the central part of the lake. While a hurricane circulates
counterclockwise and the direction of the accompanying wind generated by the hurricane
turns in a counterclockwise pattern, the magnitude of oscillation thoroughly depends on
the strength (wind speed) and the duration (length in time) of the wind to a specific
direction. In other words, the magnitude of the oscillation (height of rise and fall)
associated with the moving direction will be different at each specific location around the
lake.
4.5.3 Hurricane Katrina Traveling Along Route 3
The present model is used to study the oscillation in Lake Pontchartrain induced by wind
generated by the Route 3-traveling Hurricane Katrina (see Figure 4.28). The dimensions
of the uniform rectangular control-volumes (CV’s) in a Cartesian grid
are( ) ( ) m m y x 750 , 750 , = ∆ ∆ . The time-step t ∆ is chosen to be 45 seconds. The bathymetry
of Lake Pontchartrain adopted from the Interagency Performance Evaluation Task Force
138
(IPET) report is used in the numerical simulations (see Figure 4.14). The time-period in
the numerical simulations for the oscillation in Lake Pontchartrain induced by wind
generated by the Route 3-traveling Hurricane Katrina is from 12:00 am UTC
(Coordinated Universal Time) August 29, 2005 to 12:00 am UTC August 30, 2005, or
07:00 pm CDT (Central Daylight Time) August 28, 2005 to 07:00 pm CDT August 29,
2005. During this 24-hours time-period, Hurricane Katrina will make its landfall at
Southeast Louisiana and will pass over the west shore and its surround regions of Lake
Pontchartrain (see Figures 4.2 and 4.28). Hence, the study of the oscillation in Lake
Pontchartrain induced by wind generated by the Route 3-traveling Hurricane Katrina can
be concentrated in this 24-hours period. In order to study the oscillation phenomena in
Lake Pontchartrain induced by the Route-3 traveling Hurricane Katrina, the breaches
and/or overtopping of floodwalls and levees along Lake Pontchartrain will not be
accommodated into the numerical simulations performed by the present model for this
case; hence, the water can not flow out of the lake through the entrances of the canals
connecting to the lake during the entire 24-hours period of the numerical simulations for
the oscillations of Lake Pontchartrain induced by the Route-3 traveling Hurricane
Katrina.
The wind field inducing the oscillations in Lake Pontchartrain is exclusively caused by
the Route 3-traveling Hurricane Katrina. The numerical typhoon (or hurricane) model,
based on Equation (3.9) through Equation (3.14) in Chapter 3 and developed along with
the present model in this study, is used to generate the pressure and wind fields. The
139
meteorological data to simulate Hurricane Katrina between 12:00 am UTC August 29,
2005 and 12:00 am UTC August 30, 2005 are adopted from the Interagency Performance
Evaluation Task Force (IPET) report and are listed in Table 4.1. The diameters of the eye
of the simulated Hurricane Katrina by the numerical hurricane model are the distances
corresponding to a time interval of a half-hour traveling of the simulated Hurricane
Katrina. The speeds for the simulated Hurricane Katrina derived from the moving path
of Hurricane Katrina between 12:00 am UTC August 29, 2005 and 12:00 am UTC
August 30, 2005 are interpreted from the hourly Latitudes and Longitudes of Hurricane
Katrina recorded in the Interagency Performance Evaluation Task Force (IPET) report.
The computed hydrograph (solid black line) obtained from the present model for the 17
th
Street Canal is presented on Figure 4.100. From Figure 4.100, it is seen that the peak
water surface elevation (WSE, so called water level in the IPET report) computed by the
present model is approximately 3.11 m at the 17
th
Street Canal site. In addition, it is seen
that an abrupt fall and rise of water level (2.73 m) within 2 hours is computed by the
present model at the 17
th
Street Canal site; in other words, this sudden change of water
surface elevation (WSE) can caused a severe damage to the ships mooring around the
entrance of the 17
th
Street Canal. Furthermore, it is seen that the peak water surface
elevation induced by the Route 3-traveling Hurricane Katrina is lower than the peak
water surface level induced by the Route 1-traveling Hurricane Katrina at the 17
th
Street
Canal site (3.11 m versus 3.30 m) after comparing the computed hydrograph made under
the wind generated by the Route 3-traveling Hurricane Katrina with the one made under
140
the wind generated by the Route 1-traveling Hurricane Katrina (see the solid red line on
Figure 4.100); besides, the general trend of the fall and rise of water level induced by the
wind generated by the Route 3-traveling Hurricane Katrina is entirely different from the
general trend of the rise and fall of water level induced by the wind generated by the
Route 1-traveling Hurricane Katrina. Therefore, it can be claimed that these evident
differences in water surface elevation is caused by a hurricane passing over Lake
Pontchartrain with another route although the strength (pressure and wind speed) of the
simulated Hurricane Katrina is identical to the original one.
Figure 4.100 Computed Hydrograph, 17
th
Street Canal
141
The computed hydrograph (solid black line) obtained from the present model for the
Orleans Avenue Canal is presented on Figure 4.101. From Figure 4.101, it is seen that
the peak water surface elevation (WSE, so called water level in the IPET report)
computed by the present model is approximately 3.19 m at the Orleans Avenue Canal
site. In addition, it is seen that an abrupt fall and rise of water level (2.89 m) within 2
hours is computed by the present model at the Orleans Avenue Canal site; in other words,
this sudden change of water surface elevation (WSE) can caused a severe damage to the
ships mooring around the entrance of the Orleans Avenue Canal. Furthermore, it is seen
that the peak water surface elevation induced by the Route 3-traveling Hurricane Katrina
is lower than the peak water surface level induced by the Route 1-traveling Hurricane
Katrina at the Orleans Avenue Canal site (3.19 m versus 3.27 m) after comparing the
computed hydrograph made under the wind generated by the Route 3-traveling Hurricane
Katrina with the one made under the wind generated by the Route 1-traveing Hurricane
Katrina (see the solid red line on Figure 4.101); besides, the general trend of the fall and
rise of water level induced by the wind generated by the Route 3-traveling Hurricane
Katrina is entirely different from the general trend of the rise and fall of water level
induced by the wind generated by the Route 1-traveling Hurricane Katrina. Therefore, it
can be claimed that hurricane passing over Lake Pontchartrain with another route can
cause evident differences in water surface elevation although the strength (pressure and
wind speed) of the simulated Hurricane Katrina is identical to the original one.
142
Figure 4.101 Computed Hydrograph, Orleans Avenue Canal
The computed hydrograph (solid black line) obtained from the present model for the
London Avenue Canal is presented on Figure 4.102. From Figure 4.102, it is seen that
the peak water surface elevation (WSE, so called water level in the IPET report)
computed by the present model is approximately 3.23 m at the London Avenue Canal
site. In addition, it is seen that an abrupt fall and rise of water level (2.97 m) within 2
hours is computed by the present model at the London Avenue Canal site; in other words,
this sudden change of water surface elevation (WSE) can caused a severe damage to the
ships mooring around the entrance of the London Avenue Canal. Furthermore, it is seen
that the peak water surface elevation induced by the Route 3-traveling Hurricane Katrina
is lower than the peak water surface level induced by the Route 1-traveling Hurricane
143
Katrina at the London Avenue Canal site (3.23 m versus 3.30 m) after comparing the
computed hydrograph made under the wind generated by the Route 3-traveling Hurricane
Katrina with the one made under the wind generated by the original Hurricane Katrina
(see the solid red line on Figure 4.102); besides, the general trend of the fall and rise of
water level induced by the wind generated by the Route 3-traveling Hurricane Katrina is
entirely different from the general trend of the rise and fall of water level induced by the
wind generated by the Route 1-traveling Hurricane Katrina. Therefore, it can be claimed
that these evident differences in water surface elevation is caused by a hurricane passing
over Lake Pontchartrain with another route although the strength (pressure and wind
speed) of the simulated Hurricane Katrina is identical to the original one.
Figure 4.102 Computed Hydrograph, London Avenue Canal
144
The computed hydrograph (solid black line) obtained from the present model for the
IHNC-Lakefront Airport is presented on Figure 4.103. From Figure 4.103, it is seen that
the peak water surface elevation (WSE, so called water level in the IPET report)
computed by the present model is approximately 3.33 m at the IHNC-Lakefront Airport
site. In addition, it is seen that an abrupt fall and rise of water level (3.17 m) within 2
hours is computed by the present model at the IHNC-Lakefront Airport site; in other
words, this sudden change of water surface elevation (WSE) can caused a severe damage
to the ships mooring around the entrance of the Inner Harbor Navigation Canal (IHNC).
Furthermore, it is seen that the peak water surface elevation induced by the Route 3-
travelingHurricane Katrina is slightly higher than the peak water surface level induced by
the Route 1-traveling Hurricane Katrina at the IHNC-Lakefront Airport site (3.33 m
versus 3.30 m) after comparing the computed hydrograph made under the wind generated
by the Route 3-traveling Hurricane Katrina with the one made under the wind generated
by the Route 1-traveling Hurricane Katrina (see the solid red line on Figure 4.103);
however, the general trend of the fall and rise of water level induced by the wind
generated by the Route 3-traveling Hurricane Katrina is entirely different from the
general trend of the rise and fall of water level induced by the wind generated by the
Route 1-traveling Hurricane Katrina. Therefore, it can be claimed that hurricane passing
over Lake Pontchartrain with another route can cause evident differences in water surface
elevation although the strength (pressure and wind speed) of the simulated Hurricane
Katrina is identical to the original one.
145
Figure 4.103 Computed Hydrograph, IHNC-Lakefront Airport
The computed hydrograph (solid black line) obtained from the present model for the
Midlake is presented on Figure 4.104. From Figure 4.104, it is seen that the peak water
surface elevation induced by the Route 3-traveling Hurricane Katrina is higher than the
peak water surface level induced by the Route 1-traveling Hurricane Katrina at the
Midlake site after comparing the computed hydrograph made under the wind generated
by the Route 3-traveling Hurricane Katrina with the one made under the wind generated
by the Route 1-traveling Hurricane Katrina (see the solid red line on Figure 4.104).
Furthermore, the general trend of the rise and fall of water level induced by the wind
generated by the Route 3-traveling Hurricane Katrina is evidently different from the
general trend of the rise and fall of water level induced by the wind generated by the
146
Route 1-traveling Hurricane Katrina. Therefore, it can be claimed that these significant
differences in the water surface elevations are caused by a hurricane passing over Lake
Pontchartrain with another route although the strength (pressure and wind speed) of the
simulated Hurricane Katrina is identical to the original one.
Figure 4.104 Computed Hydrograph, Midlake
The computed hydrograph (solid black line) obtained from the present model for Bayou
La Branche (named Bayou Labranch in the IPET report) is presented on Figure 4.105. It
can be seen from Figures 4.7 and 4.13 that Bayou La Branche is in the swamp along the
southwest shore of Lake Pontchartrain and the swamps along the entire southwest shore
of Lake Pontchatrain have been assigned into the computational domain for the current
147
numerical simulations performed by the FVM model. From Figure 4.105, it is seen that
the peak water surface elevation induced by the Route 3-traveling Hurricane Katrina is
much higher than the peak water surface level induced by the Route 1-traveling
Hurricane Katrina at Bayou La Branche site after comparing the computed hydrograph
made under the wind generated by the Route 3-traveling Hurricane Katrina with the one
made under the wind generated by the Route 1-traveling Hurricane Katrina (see the solid
red line on Figure 4.105). Besides, the general trends of the rise and fall of water levels
on both computed hydrographs (solid black and solid red lines on Figure 4.105) made by
the present model are almost identical although the highest water surface elevations
induced by the winds generated by two hurricanes (Route 3-traveling Katrina and Route
1-travling Katrina) are slightly different at Bayou La Branche site. Therefore, it can be
claimed that this evident difference in the water surface elevation is caused by a hurricane
passing over Lake Pontchartrain with another route although the strength (pressure and
wind speed) of the simulated Hurricane Katrina is identical to the original one.
148
Figure 4.105 Computed Hydrograph, Bayou La Branche
The computed hydrograph (solid black line) obtained from the present model for Pass
Manchac-Turtle Cove is presented on Figure 4.106. From Figures 4.7 and 4.13, it can be
seen that Pass Manchac is a the narrow strip of water connecting Lake Pontchartrain and
Lake Maurepas and the entire Pass Manchac is included in the computational domain
used in the current numerical simulations performed by the present model. From Figure
4.106, it is seen that the peak water surface elevation induced by the Route 3-traveling
Hurricane Katrina is much higher than the peak water surface level induced by the
original Hurricane Katrina at Pass Manchac-Turtle Cove site after comparing the
computed hydrograph made under the wind generated by the Route 3-traveling Hurricane
Katrina with the one made under the wind generated by the Route 1-traveling Hurricane
149
Katrina (see the solid red line on Figure 4.106). Besides, the general trend of the rise and
fall of water level induced by the wind generated by the Route 3-traveling Hurricane
Katrina is entirely different from the general trend of the rise and fall of water level
induced by the wind generated by the Route 1-traveling Hurricane Katrina. Therefore, it
can be claimed that this significant difference in the water surface elevation is caused by
a hurricane passing over Lake Pontchartrain with another route although the strength
(pressure and wind speed) of the simulated Hurricane Katrina is identical to the original
one.
Figure 4.106 Computed Hydrograph, Pass Manchac-Turtle Cove
150
The computed hydrograph (solid black line) obtained from the present model for Little
Irish Bayou is presented on Figure 4.107. From Figure 4.107, it is seen that the peak
water surface elevation induced by the Route 3-traveling Hurricane Katrina is much
higher than the peak water surface level induced by the Route 1-traveling Hurricane
Katrina at Little Irish Bayou site after comparing the computed hydrograph made under
the wind generated by the Route 3-traveling Hurricane Katrina with the one made under
the wind generated by the Route 1-traveling Hurricane Katrina (see the solid red line on
Figure 4.107). Besides, the general trends of the rise and fall of water levels on both
computed hydrographs (solid black and solid red lines on Figure 4.107) made by the
present model are almost identical although the highest water surface elevations induced
by the winds generated by two hurricanes (Route 3-traveling Katrina and Route 1-
travling Katrina) are slightly different at Little Irish Bayou site. Therefore, it can be
claimed that this evident difference in the water surface elevation is caused by a hurricane
passing over Lake Pontchartrain with another route although the strength (pressure and
wind speed) of the simulated Hurricane Katrina is identical to the original one.
151
Figure 4.107 Computed Hydrograph, Little Irish Bayou
The computed hydrographs of the water surface elevation (WSE) showing on S-N and
W-E cross-sections of Lake Pontchartrain induced by the wind generated through the
Route 3 –Traveling Hurricane Katrina (see Figure 4.28) are presented on Figures 4.108
and 4.109, respectively. It is seen from Figures 4.108 and 4.109 that the wind-induced
oscillations in Lake Pontchartrain are the evident phenomena as Hurricane Katrina
progressed over the west shore and its surrounding regions of Lake Pontchartrain (Route
3 shown in Figure 4.28). In the following paragraphs, the hourly contour maps of the
water surface elevation (WSE) for the entire Lake Pontchartrain, as Hurricane Katrina
progressed over the west shore and its surrounding regions of Lake Pontchartrain (Route
152
3 shown in Figure 4.28), are used to investigate the oscillations of semi-enclosed water
body induced by hurricanes under specific routes.
The hourly contour maps of the computed water surface elevation (WSE) for the entire
Lake Pontchartrain induced by the wind generated through the Route 3-traveling
Hurricane Katrina are presented from Figures 4.110 to Figures 4.134. The time-frame of
these contour maps is from 12:00 am UTC August 29, 2005 to 12:00 am UTC August 30,
2005. It is assigned that 0 t = is at 11:59:15 pm UTC August 28, 2005 and consequently
the reference WSE at 0 t = is zero. Therefore, the oscillation phenomenon is not evident
throughout entire Lake Pontchartrain at the starting moment of the numerical simulation
(12:00 am August 29, 2005), as it is seen from Figure 4.110. As it is seen from Figures
4.2 and 4.28, the original Hurricane Katrina did not make its landfall until 6:10 am CDT
(11:10 am UTC) August 29 at Southeast Louisiana and the distance between the Route 1
and Route 3 is approximately 72 km; besides, the oscillation induced by tides from Gulf
of Mexico into Lake Pontchartrain is not influential in this study, this is a reasonable
assumption that the oscillations in Lake Pontchartrain induced by wind generated by the
Route 3-traveling Hurricane Katrina can be focused on the 24-hours period between
12:00 am UTC August 29, 2005 and 12:00 am UTC August 30, 2005.
153
Figure 4.108 Hydrographs of the S-N cross-section
Figure 4.109 Hydrographs of the W-E cross-section
154
Figure 4.110 Contours of WSE at 12:00 am (UTC) August 29, 2005
Figure 4.111 Contours of WSE at 01:00 am (UTC) August 29, 2005
155
Figure 4.112 Contours of WSE at 02:00 am (UTC) August 29, 2005
Figure 4.113 Contours of WSE at 03:00 am (UTC) August 29, 2005
156
Figure 4.114 Contours of WSE at 04:00 am (UTC) August 29, 2005
Figure 4.115 Contours of WSE at 05:00 am (UTC) August 29, 2005
157
Figure 4.116 Contours of WSE at 06:00 am (UTC) August 29, 2005
Figure 4.117 Contours of WSE at 07:00 am (UTC) August 29, 2005
158
Figure 4.118 Contours of WSE at 08:00 am (UTC) August 29, 2005
Figure 4.119 Contours of WSE at 09:00 am (UTC) August 29, 2005
159
Figure 4.120 Contours of WSE at 10:00 am (UTC) August 29, 2005
Figure 4.121 Contours of WSE at 11:00 am (UTC) August 29, 2005
160
Figure 4.122 Contours of WSE at 12:00 pm (UTC) August 29, 2005
Figure 4.123 Contours of WSE at 01:00 pm (UTC) August 29, 2005
161
Figure 4.124 Contours of WSE at 02:00 pm (UTC) August 29, 2005
Figure 4.125 Contours of WSE at 03:00 pm (UTC) August 29, 2005
162
Figure 4.126 Contours of WSE at 04:00 pm (UTC) August 29, 2005
Figure 4.127 Contours of WSE at 05:00 pm (UTC) August 29, 2005
163
Figure 4.128 Contours of WSE at 06:00 pm (UTC) August 29, 2005
Figure 4.129 Contours of WSE at 07:00 pm (UTC) August 29, 2005
164
Figure 4.130 Contours of WSE at 08:00 pm (UTC) August 29, 2005
Figure 4.131 Contours of WSE at 09:00 pm (UTC) August 29, 2005
165
Figure 4.132 Contours of WSE at 10:00 pm (UTC) August 29, 2005
Figure 4.133 Contours of WSE at 11:00 pm (UTC) August 29, 2005
166
Figure 4.134 Contours of WSE at 12:00 am (UTC) August 30, 2005
It can be seen from Figures 4.111 to 4.113 that the oscillation in Lake Pontchartrain is
built up as Hurricane Katrina approaches to Southeast Louisiana and it becomes more
obvious as time goes by. It is very evident that the direction of node line ( 0 = η ) in the
lake is in the North-South orientation. It is seen that the water in the east part of the lake
is driven by the wind to the west part of the lake during the first 3-hour period, as we
examine the temporal variations of the contours of WSE from 12:00 to 03:00 am UTC
August 29, 2005. The strength of Hurricane Katrina, according to the IPET report,
remains Category 4 in Saffir-Simpson Scale within this 3-hours period.
167
It is possible that the Route 3-traveling Hurricane Katrina makes its landfall at Southeast
Louisiana around 11:00 am UTC (6:00 am Local Time) August 29 since the distance
between Route 1 and Route 3 is about only 72 km (see Figures 4.2 and 4.28). As the
Route 3-traveling Hurricane Katrina approaches Southeast Louisiana, the magnitude of
oscillation in Lake Pontchartrain gradually increases between 04:00 am UTC and 09:00
am UTC August 29, 2005. During this 6-hours period, the direction of node line ( 0 = η )
in the lake slowly changes from the North-South orientation to the Northeast-Southwest
orientation since the direction of the dominant wind alters as Hurricane Katrina
approaches to Lake Pontchartrain; meanwhile, the strength of Hurricane Katrina,
according to the IPET report, is gradually reducing from Category 4 to 3 in Saffir-
Simpson Scale within this 6-hours period.. We can see these phenomena after examining
the temporal variations of the contours of WSE from Figures 4.114 to 4.119.
As the Route 3-traveling Hurricane Katrina approaches Southeast Louisiana, the
magnitude of oscillation in Lake Pontchartrain gradually increases between 09:00 am
UTC and 12:00 pm UTC August 29, 2005. During this 3-hours period, the direction of
node line ( 0 = η ) in the lake remains the Northeast-Southwest orientation although the
direction of the dominant wind alters as Hurricane Katrina approaches to Lake
Pontchartrain while its strength remains Category 3. We can see these phenomena after
examining the temporal variations of the contours of WSE from Figures 4.120 to 4.122.
168
From 12:00 pm UTC to 03:00 pm UTC August 29, the Route 3-traveling Hurricane
Katrina passes over the west shore and its surrounding regions of Lake Pontchartrain.
Thus, this close-encounter between the hurricane and the lake causes significant
oscillations in Lake Pontchartrain as we compare the oscillations happened in the lake
during the previous 12 hours. It is seen from Figures 4.123 to 4.125 that the direction of
node line ( 0 = η ) in the lake changes from the Northeast-Southwest orientation to the
nearly East-West orientation as the direction of the dominant wind rapidly alters during
this 3-hours period. Meanwhile, the magnitude of oscillation (the height of WSE)
becomes higher than the previous 3 hours, and the oscillation along the northwest and
north shores of Lake Pontchartrain reaches the highest magnitude between 02:30 and
03:00 pm UTC (or 09:30 and 10:00 am Local Time), as it is seen from the computed
hydrograph for Pass Manchac (Figure 4.106). Within this 3-hours period, the strength of
the Route 3-traveling Hurricane Katrina still remains Category 3.
During the next 3-hours period (from 03:00 to 06:00 pm UTC August 29), the Route 3-
traveling Hurricane Katrina continuously crosses over the west shore and its surrounding
regions of Lake Pontchartrain and moves inland with a nearly north direction while its
strength reduces from Category 3 to 2; in other words, the wind generated by the
hurricane gets weaker during this 3-hours time-period. Meanwhile, the direction of node
line ( 0 = η ) rapidly turns from the nearly East-West orientation in a clockwise pattern to
the nearly North-South orientation even though the direction of the dominant wind alters
169
o
90 in a counterclockwise pattern. Because the surge propagates into Lake Pontchartrain
from the Gulf of Mexico via Lake Borgne (see Figure 4.3), a huge amount of water flows
into Lake Pontchartrain and the magnitude of oscillation (the height of WSE) in Lake
Pontchartrain evidently increases even though the hurricane leaves the northwest regions
of the lake. Furthermore, the node line ( 0 = η ) disappears and the WSE in the entire lake
is greater than the reference WSE ( 0 = η ) from 05:00 pm, as it is seen from Figure 4.127.
We can find these evidences from a thorough study of the temporal variations of the
contours of WSE from Figures 4.126 to 4.128.
In the final 6-hours period (from 07:00 pm UTC August 29 to 12:00 am UTC August 30,
2005), the strength of the Route 3-traveling Hurricane Katrina continuously reduces from
Category 2 to 1; furthermore, the Route 3-traveling Hurricane Katrina becomes a tropical
storm as it moves inwardly into the northeastern region of the United States of America
as the original Hurricane Katrina moves inwardly (see Figures 4.2 and 4.28). Although
the direction of dominant wind keeps turning counterclockwise during this 6-hours
period, the wind generated by the hurricane is drastically weaker than it was in the
previous 18-hours period. Since the hurricane moves far away from the lake, the
magnitude of oscillation in Lake Pontchartrain gradually reduces and is smaller than it
was in the previous 6-hour period. Besides, the major sloshing motion is moving toward
the east within this 6-hours period. The WSE in the lake does not significantly recede
since there is not enough wind stress to drive out the water from Lake Pontchartrain to
170
Lake Borgne and other surrounding water bodies (for example, Lake Maurepas); hence,
the WSE in the entire lake is greater than the reference WSE ( 0 = η ) in this 6-hours
period. Meanwhile, there is a significant drawdown in the east portion of Lake
Pontchartrain at the finale of the numerical simulation (09:00 pm August 29 to 12:00 am
August 30, 2005) as it is seen from Figures 4.131 to 4.134. We can obtain these
discoveries by examining the temporal variations of WSE from Figures 4.129 to 4.134.
Furthermore, the significant findings drawn from these hourly contour maps (from
Figures 4.110 to 4.134) are summarized in the following paragraphs.
The Route 3-traveling Hurricane Katrina moves in a nearly north direction and passes
over the west shore and its surrounding regions of Lake Pontchartrain between 12:00 am
and 06:00 pm UTC August 29, 2005 corresponding to the first 18-hours of the numerical
simulations made by the present model. The closest encounter between Hurricane
Katrina and Lake Pontchartrain takes place between 12:00 and 06:00 pm UTC (or 7:00
am and 1:00 pm Local Time) August 29, 2005 (see Figure 4.2). During this 6-hours
period, there are three significant factors of Hurricane Katrina needed to be reviewed:
1. The hurricane remains Category 3 intensity of Saffir-Simpson Scale until 03:00
pm UTC (10:00 am Local Time), after which the strength of the hurricane
gradually reduces to Category 2.
2. The hurricane is moving in a nearly north direction with an approximate speed of
27 to 29 km/hr.
3. The eye of the Route 3-traveling Hurricane Katrina passes through the west shore
of Lake Pontchartrain.
171
Because of these three unique characteristics of the interaction between the hurricane and
the lake, the sloshing motion of the lake water surface changes in a clockwise pattern in
the lake; however, the hurricane itself rotates in the counterclockwise character. In detail,
the dominant sloshing motion at Lake Pontchartrain turns from the northwest to the east
within this 6-hours period. During this 6-hours, the lowest amplitude of oscillation
(minimum WSE) along the south shore of the lake happens between 02:30 and 03:00 pm
UTC (between 09:30 and 10:00 am Local Time); on the contrary, the highest measured
water level along the south shore of Lake Pontchartrain during the invasion of the
original Hurricane Katrina (Route 1-traveling Hurricane Katrina) happens during this 6-
hours period (Route 1 shown in Figure 4.28). Meanwhile, the highest amplitude of
oscillation (maximum WSE) along the south shore of the lake happens between 03:00
and 03:30 pm UTC (between 10:00 and 10:30 am Local Time) with a magnitude of 3.11
m to 3.33 m predicted by the present model.
Furthermore, the moving direction of the storm surge changes from the west direction to
the east direction within the first 16-hours period (12:00 am to 04:00 pm UTC August 29,
2005) of the numerical simulations (see Figures 4.110 to 126); in other words, the
sloshing motion changes
o
180 in 16 hours. Besides, the oscillation (rise and fall of water
level) in a semi-enclosed lake induced by a hurricane can be moving around the lake in a
clockwise-turning pattern although the direction of dominant wind generated by the
hurricane alters in a counterclockwise pattern. In detail, the moving direction of the
oscillation of a semi-enclosed water body induced by a hurricane rotates in a clockwise
172
pattern even though a hurricane circulates counterclockwise and the direction of the
accompanying wind generated by the hurricane can turn in a counterclockwise pattern.
Meanwhile, the magnitude of oscillation thoroughly depends on the strength (wind speed)
and the duration (length in time) of the wind to a specific direction; in detail, the
magnitude of the oscillation (height of rise and fall) associated with the moving direction
will be different at each specific location around the lake.
4.5.4 Hurricane Katrina Traveling With Reduced Forward Speeds
The present model is used to study the oscillation in Lake Pontchartrain induced by wind
generated by the Route 1-traveling Hurricane Katrina with reduced forward speeds (see
Figure 4.28). The dimensions of the uniform rectangular control-volumes (CV’s) in a
Cartesian grid are( ) ( ) m m y x 750 , 750 , = ∆ ∆ . The time-step t ∆ is chosen to be 45 seconds.
The bathymetry of Lake Pontchartrain adopted from the Interagency Performance
Evaluation Task Force (IPET) report is used in the numerical simulations (see Figure
4.14). The time-period in the numerical simulations for the oscillation in Lake
Pontchartrain induced by wind generated by the Route 1-traveling Hurricane Katrina with
reduced forward speeds is from 12:00 am UTC (Coordinated Universal Time) August 29,
2005 to 12:00 am UTC August 30, 2005, or 07:00 pm CDT (Central Daylight Time)
August 28, 2005 to 07:00 pm CDT August 29, 2005. During this 24-hours time-period,
Hurricane Katrina will make two landfalls at Southeast Louisiana and will pass through
173
the region along the east shore of Lake Pontchartrain (see Figures 4.2 and 4.28). Hence,
the study of the oscillation in Lake Pontchartrain induced by wind generated by the Route
1-traveling Hurricane Katrina with reduced forward speeds can be concentrated in this
24-hours period. In order to study the oscillation phenomena in Lake Pontchartrain
induced by the Route-1 traveling Hurricane Katrina with reduced forward speeds, the
breaches and/or overtopping of floodwalls and levees along Lake Pontchartrain will not
be accommodated into the numerical simulations performed by the present model for this
case; hence, the water can not flow out of the lake through the entrances of the canals
connecting to the lake during the entire 24-hours period of the numerical simulations for
the oscillations of Lake Pontchartrain induced by the Route-1 traveling Hurricane Katrina
with reduced forward speeds.
The wind field inducing the oscillations in Lake Pontchartrain is exclusively caused by
the Route 1-traveling Hurricane Katrina with reduced forward speeds. The numerical
typhoon (or hurricane) model, based on Equation (3.9) through Equation (3.14) in
Chapter 3 and developed along with the present model in this study, is used to generate
the pressure and wind fields. The necessary meteorological data to simulate Hurricane
Katrina between 12:00 am UTC August 29, 2005 and 12:00 am UTC August 30, 2005
are adopted and modified from the Interagency Performance Evaluation Task Force
(IPET) report and are listed in Table 4.2. The diameters of the eye of the simulated
Hurricane Katrina by the numerical hurricane model are the distances corresponding to a
time interval of a half-hour traveling of the simulated Hurricane Katrina. The forward
174
speeds for the simulated Hurricane Katrina derived from the moving path of the original
Hurricane Katrina between 12:00 am UTC August 29, 2005 and 12:00 am UTC August
30, 2005 are interpreted and adjusted from the hourly Latitudes and Longitudes of
Hurricane Katrina recorded in the Interagency Performance Evaluation Task Force
(IPET) report for the numerical simulation.
Table 4.2 Characteristics of a Hurricane Required in the Numerical Simulation
Date/Time (UTC) Central Pressure (bar) Radius to Maximum Winds (m)
Aug 29 0000 90400 34000
Aug 29 0300 90600 34000
Aug 29 0600 90800 34000
Aug 29 0900 91000 34000
Aug 29 1200 91350 47000
Aug 29 1500 91700 58000
Aug 29 1800 92300 67000
Aug 29 2100 93200 37000
Aug 30 0000 94800 42000
The computed hydrograph (solid black line) obtained from the present model for the 17
th
Street Canal is presented on Figure 4.135. From Figure 4.135, it is seen that the peak
water surface elevation (WSE, so called water level in the IPET report) computed by the
present model is approximately 4.45 m at the 17
th
Street Canal site. Besides, it is seen
that the peak water surface elevation induced by the Route 1-traveling Hurricane Katrina
with reduced forward speeds is much larger than the peak water surface level induced by
the Route 1-traveling Hurricane Katrina at the 17
th
Street Canal site (4.45 m versus 3.30
m) after comparing the computed hydrograph made under the wind generated by the
hurricane with the one made under the wind generated by the Route 1-traveling
175
Hurricane Katrina (see the solid red line on Figure 4.135). Therefore, it can be claimed
that this significant difference in water surface elevation is caused by a hurricane passing
over Lake Pontchartrain with different forward speeds although the strength (pressure
and wind speed) of the simulated Hurricane Katrina is identical to the original one.
Figure 4.135 Computed Hydrograph, 17
th
Street Canal
The computed hydrograph (solid black line) obtained from the present model for the
Orleans Avenue Canal is presented on Figure 4.136. From Figure 4.136, it is seen that
the peak water surface elevation (WSE, so called water level in the IPET report)
computed by the present model is approximately 4.39 m at the Orleans Avenue Canal
site. Besides, it is seen that the peak water surface elevation induced by the Route 1-
176
traveling Hurricane Katrina with reduced forward speeds is much larger than the peak
water surface level induced by the Route 1-travling Hurricane Katrina at the Orleans
Avenue Canal site (4.39 m versus 3.27 m) after comparing the computed hydrograph
made under the wind generated by the hurricane with the one made under the wind
generated by the original Hurricane Katrina (see the solid red line on Figure 4.136).
Therefore, it can be claimed that hurricane passing over Lake Pontchartrain with different
forward speeds another route can cause a significant difference in water surface elevation
although the strength (pressure and wind speed) of the simulated Hurricane Katrina is
identical to the original one.
Figure 4.136 Computed Hydrograph, Orleans Avenue Canal
177
The computed hydrograph (solid black line) obtained from the present model for the
London Avenue Canal is presented on Figure 4.137. From Figure 4.137, it is seen that
the peak water surface elevation (WSE, so called water level in the IPET report)
computed by the present model is approximately 4.40 m at the London Avenue Canal
site. Besides, it is seen that the peak water surface elevation induced by the Route 1-
traveling Hurricane Katrina with reduced forward speeds is much larger than the peak
water surface level induced by the Route 1-traveling Hurricane Katrina at the London
Avenue Canal site (4.40 m versus 3.30 m) after comparing the computed hydrograph
made under the wind generated by the hurricane with the one made under the wind
generated by the original Hurricane Katrina (see the solid red line on Figure 4.137).
Therefore, it can be claimed that this evident difference in water surface elevation is
caused by a hurricane passing over Lake Pontchartrain with different forward speeds
although the strength (pressure and wind speed) of the simulated Hurricane Katrina is
identical to the original one.
178
Figure 4.137 Computed Hydrograph, London Avenue Canal
The computed hydrograph (solid black line) obtained from the present model for the
IHNC-Lakefront Airport is presented on Figure 4.138. From Figure 4.138, it is seen that
the peak water surface elevation (WSE, so called water level in the IPET report)
computed by the present model is approximately 4.33 m at the IHNC-Lakefront Airport
site. Besides, it is seen that the peak water surface elevation induced by the Route 1-
traveling Hurricane Katrina with reduced forward speeds is much larger than the peak
water surface level induced by the Route 1-traveling Hurricane Katrina at the IHNC-
Lakefront Airport site (4.33 m versus 3.30 m) after comparing the computed hydrograph
made under the wind generated by the hurricane with the one made under the wind
generated by the Route 1-traveling Hurricane Katrina (see the solid red line on Figure
179
4.138). Therefore, it can be claimed that hurricane passing over Lake Pontchartrain with
different forward speeds can cause an evident difference in water surface elevation
although the strength (pressure and wind speed) of the simulated Hurricane Katrina is
identical to the original one.
Figure 4.138 Computed Hydrograph, IHNC-Lakefront Airport
The computed hydrograph (solid black line) obtained from the present model for the
Midlake is presented on Figure 4.139. From Figure 4.139, it is seen that the peak water
surface elevation induced by the Route 1-traveling Hurricane Katrina with reduced
forward speeds is much larger than the peak water surface level induced by the Route 1-
traveling Hurricane Katrina at the Midlake site after comparing the computed hydrograph
180
made under the wind generated by the hurricane with the one made under the wind
generated by the Route 1-traveling Hurricane Katrina (see the solid red line on Figure
4.139). Furthermore, the general trend of the rise and fall of water level induced by the
wind generated by the Route 1-traveling Hurricane Katrina with reduced forward speeds
is slightly different from the general trend of the rise and fall of water level induced by
the wind generated by the Route 1-traveling Hurricane Katrina. Therefore, it can be
claimed that these evident differences in the water surface elevations are caused by a
hurricane passing over Lake Pontchartrain with different forward speeds although the
strength (pressure and wind speed) of the simulated Hurricane Katrina is identical to the
original one.
Figure 4.139 Computed Hydrograph, Midlake
181
The computed hydrograph (solid black line) obtained from the present model for Bayou
La Branche (named Bayou Labranch in the IPET report) is presented on Figure 4.140. It
can be seen from Figures 4.7 and 4.13 that Bayou La Branche is in the swamp along the
southwest shore of Lake Pontchartrain and the swamps along the entire southwest shore
of Lake Pontchatrain have been assigned into the computational domain for the current
numerical simulations performed by the FVM model. From Figure 4.140, it is seen that
the peak water surface elevation induced by the Route 1-traveling Hurricane Katrina with
reduced forward speeds is much larger than the peak water surface level induced by the
Route 1-traveling Hurricane Katrina at Bayou La Branche site after comparing the
computed hydrograph made under the wind generated by the hurricane with the one made
under the wind generated by the Route 1-traveling Hurricane Katrina (see the solid red
line on Figure 4.140); besides, the moments at which the highest water surface elevations
induced by the winds generated by two hurricanes (Route 1-traveling Katrina with
reduced forward speeds and Route 1-traveling Katrina) happen at Bayou La Branche site
are not within the same period of time. Furthermore, the general trends of the rise and
fall of water levels on both computed hydrographs (solid black and solid red lines on
Figure 4.140) made by the present model are completely different at Bayou La Branche
site. Therefore, it can be claimed that these evident differences in the water surface
elevation are caused by a hurricane passing over Lake Pontchartrain with different
forward speeds although the strength (pressure and wind speed) of the simulated
Hurricane Katrina is identical to the original one.
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Figure 4.140 Computed Hydrograph, Bayou La Branche
The computed hydrograph (solid black line) obtained from the present model for Pass
Manchac-Turtle Cove is presented on Figure 4.141. From Figures 4.7 and 4.13, it can be
seen that Pass Manchac is a the narrow strip of water connecting Lake Pontchartrain and
Lake Maurepas and the entire Pass Manchac is included in the computational domain
used in the current numerical simulations performed by the present model. From Figure
4.141, it is seen that the peak water surface elevation induced by the Route 1-traveling
Hurricane Katrina with reduced forward speeds is almost equal to the peak water surface
level induced by the Route 1-traveling Hurricane Katrina at Pass Manchac-Turtle Cove
site after comparing the computed hydrograph made under the wind generated by the
hurricane with the one made under the wind generated by the Route 1-traveling
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Hurricane Katrina (see the solid red line on Figure 4.141); however, the moments at
which the highest water surface elevations induced by the winds generated by two
hurricanes (Route 1-traveling Katrina with reduced moving speeds and Route 1-traveling
Katrina) happen at Pass Manchac-Turtle Cove site are not within the same period of time.
Besides, the general trends of the rise and fall of water levels on both computed
hydrographs (solid black and solid red lines on Figure 4.141) made by the present model
are entirely different at Pass Manchac-Turtle Cove site. Therefore, it can be claimed that
these evident differences in the water surface elevation are caused by a hurricane passing
over Lake Pontchartrain with different forward speeds although the strength (pressure
and wind speed) of the simulated Hurricane Katrina is identical to the original one.
Figure 4.141 Computed Hydrograph, Pass Manchac-Turtle Cove
184
The computed hydrograph (solid black line) obtained from the present model for Little
Irish Bayou is presented on Figure 4.142. From Figure 4.142, it is seen that the peak
water surface elevation induced by the Route 1-traveling Hurricane Katrina with reduced
forward speeds is much larger than the peak water surface level induced by the Route 1-
traveling Hurricane Katrina at Little Irish Bayou site after comparing the computed
hydrograph made under the wind generated by the hurricane with the one made under the
wind generated by the Route 1-traveling Hurricane Katrina (see the solid red line on
Figure 4.142). Besides, the general trends of the rise and fall of water levels on both
computed hydrographs (solid black and solid red lines on Figure 4.142) made by the
present model are almost identical although the moments at which the highest water
surface elevations induced by the winds generated by two hurricanes (Route 1-traveling
Katrina with reduced forward speeds and Route 1-traeling Katrina) happen at Little Irish
Bayou site are not within the same period of time. Therefore, it can be claimed that these
evident differences in the water surface elevation are caused by a hurricane passing over
Lake Pontchartrain with different forward speeds although the strength (pressure and
wind speed) of the simulated Hurricane Katrina is identical to the original one.
185
Figure 4.142 Computed Hydrograph, Little Irish Bayou
The computed hydrographs of the water surface elevation (WSE) showing on S-N and
W-E cross-sections of Lake Pontchartrain induced by the wind generated through the
Route 1 –Traveling Hurricane Katrina with reduced forward speeds (see Figure 4.28) are
presented on Figures 4.143 and 4.144, respectively. It is seen from Figures 4.143 and
4.144 that the wind-induced oscillations in Lake Pontchartrain are the evident phenomena
as the Hurricane Katrina with reduced forward speeds progressed over the Southeast
Louisiana region (Route 1 shown in Figure 4.28). In the following paragraphs, the hourly
contour maps of the water surface elevation (WSE) for the entire Lake Pontchartrain, as
the Hurricane Katrina with reduced forward speeds progressed over the Southeast
Louisiana region (Route 1 shown in Figure 4.28), are used to investigate the oscillations
186
of semi-enclosed water body induced by hurricanes under specific routes and different
forward speeds.
The hourly contour maps of the computed water surface elevation (WSE) for the entire
Lake Pontchartrain induced by the wind generated through the Route 1-traveling
Hurricane Katrina with reduced forward speeds are presented from Figures 4.145 to
Figures 4.169. The time-frame of these contour maps is from 12:00 am UTC August 29,
2005 to 12:00 am UTC August 30, 2005. It is assigned that 0 t = is at 11:59:15 pm UTC
August 28, 2005 and consequently the reference WSE at 0 t = is zero. Therefore, the
oscillation phenomenon is not evident throughout entire Lake Pontchartrain at the starting
moment of the numerical simulation (12:00 am August 29, 2005), as it is seen from
Figure 4.145. Because the Route 1-traveling Hurricane Katrina with reduced forward
speeds might make its first landfall around 8:40 am CDT (13:40 am UTC) August 29 at
Southeast Louisiana and the oscillation induced by tides from Gulf of Mexico into Lake
Pontchartrain is not an influential factor in this study, this is a reasonable assumption that
the oscillations in Lake Pontchartrain induced by wind generated by the Route 1-traveling
Hurricane Katrina with reduced forward speeds can be focused on the 24-hours period
between 12:00 am UTC August 29, 2005 and 12:00 am UTC August 30, 2005.
187
Figure 4.143 Hydrographs of the S-N cross-section
Figure 4.144 Hydrographs of the W-E cross-section
188
Figure 4.145 Contours of WSE at 12:00 am (UTC) August 29, 2005
Figure 4.146 Contours of WSE at 01:00 am (UTC) August 29, 2005
189
Figure 4.147 Contours of WSE at 02:00 am (UTC) August 29, 2005
Figure 4.148 Contours of WSE at 03:00 am (UTC) August 29, 2005
190
Figure 4.149 Contours of WSE at 04:00 am (UTC) August 29, 2005
Figure 4.150 Contours of WSE at 05:00 am (UTC) August 29, 2005
191
Figure 4.151 Contours of WSE at 06:00 am (UTC) August 29, 2005
Figure 4.152 Contours of WSE at 07:00 am (UTC) August 29, 2005
192
Figure 4.153 Contours of WSE at 08:00 am (UTC) August 29, 2005
Figure 4.154 Contours of WSE at 09:00 am (UTC) August 29, 2005
193
Figure 4.155 Contours of WSE at 10:00 am (UTC) August 29, 2005
Figure 4.156 Contours of WSE at 11:00 am (UTC) August 29, 2005
194
Figure 4.157 Contours of WSE at 12:00 pm (UTC) August 29, 2005
Figure 4.158 Contours of WSE at 01:00 pm (UTC) August 29, 2005
195
Figure 4.159 Contours of WSE at 02:00 pm (UTC) August 29, 2005
Figure 4.160 Contours of WSE at 03:00 pm (UTC) August 29, 2005
196
Figure 4.161 Contours of WSE at 04:00 pm (UTC) August 29, 2005
Figure 4.162 Contours of WSE at 05:00 pm (UTC) August 29, 2005
197
Figure 4.163 Contours of WSE at 06:00 pm (UTC) August 29, 2005
Figure 4.164 Contours of WSE at 07:00 pm (UTC) August 29, 2005
198
Figure 4.165 Contours of WSE at 08:00 pm (UTC) August 29, 2005
Figure 4.166 Contours of WSE at 09:00 pm (UTC) August 29, 2005
199
Figure 4.167 Contours of WSE at 10:00 pm (UTC) August 29, 2005
Figure 4.168 Contours of WSE at 11:00 pm (UTC) August 29, 2005
200
Figure 4.169 Contours of WSE at 12:00 am (UTC) August 30, 2005
It can be seen from Figures 4.146 to 4.151 that the oscillation in Lake Pontchartrain is
built up as the Route 1-traveling Hurricane Katrina with reduced forward speeds
approaches to Southeast Louisiana and it becomes more obvious as time goes by. It is
very evident that the direction of node line ( 0 = η ) in the lake is in the North-South
orientation. It is seen that the water in the east part of the lake is driven by the wind to
the west part of the lake during the first 6-hour period, as we examine the temporal
variations of the contours of WSE from 12:00 to 06:00 am UTC August 29, 2005. The
strength of the Route 1-traveling Hurricane Katrina with reduced forward speeds remains
Category 4 in Saffir-Simpson Scale within this 6-hours period.
201
As the Route 1-traveling Hurricane Katrina with reduced forward speeds approaches to
Southeast Louisiana, the magnitude of oscillation in the lake gradually increases between
07:00 am UTC and 12:00 pm UTC August 29, 2005. During this 6-hours period, the
direction of node line ( 0 = η ) in the lake slowly changes from the North-South
orientation to the Northwest-Southeast orientation since the direction of the dominant
wind alters as the hurricane approaches to Lake Pontchartrain; meanwhile, the strength of
the hurricane is gradually reducing from Category 4 to 3 in Saffir-Simpson Scale. We
can see these phenomena after examining the temporal variations of the contours of WSE
from Figures 4.152 to 4.157.
From 12:00 pm UTC to 03:00 pm UTC August 29, the Route 1-traveling Hurricane
Katrina with reduced forward speeds approaches to Southeast Louisiana and might make
its first landfall at approximately 13:40 pm UTC (8:40 am Local Time); meanwhile, the
strength of the Route 1-traveling Hurricane Katrina with reduced forward speeds still
remains Category 3. Thus, the magnitude of oscillation in the lake evidently increases as
it is compared with the oscillations happened in the lake during the previous 12 hours. It
is seen from Figures 4.158 to 4.160 that the direction of node line ( 0 = η ) in the lake
remains in the Northwest-Southeast orientation although the direction of the dominant
wind rapidly alters in a counterclockwise pattern during this 3-hours period.
During the next 3-hours period (from 03:00 to 06:00 pm UTC August 29), Hurricane
Katrina passes nearby the east shore and its surrounding regions of Lake Pontchartrain.
202
Thus, this close-encounter between the hurricane and the lake causes significant
oscillations in Lake Pontchartrain as we compare the oscillations happened in the lake
during the previous 15 hours. It is seen from Figures 4.161 to 4.163 that the direction of
node line ( 0 = η ) in the lake changes from the Northwest-Southeast orientation to the
West-East orientation as the direction of the dominant wind rapidly alters during this 3-
hours period. Meanwhile, the magnitude of oscillation (the height of WSE) becomes
higher than the previous 3 hours, and the oscillation along the south shore of Lake
Pontchartrain reaches the highest magnitude around 06:00 pm UTC (1:00 pm Local
Time), as we have already seen from Figures 4.161 to 4.163. Within this 3-hours period,
the Route 1-traveling Hurricane Katrina with reduced forward speeds still remains
Category 3.
From 06:00 pm UTC to 09:00 pm UTC August 29, the Route 1-traveling Hurricane
Katrina with reduced forward speeds continuously moves inland with a north direction
and might make its second landfall at approximately 06:40 pm UTC (01:40 pm Local
Time) near Louisiana/Mississippi border; meanwhile, the strength of the Route 1-
traveling Hurricane Katrina with reduced forward speeds still remains Category 3. It is
seen from Figures 4.164 to 4.166 that the direction of node line ( 0 = η ) changes from the
West-East orientation to the Southwest-Northeast orientation as the direction of the
dominant wind rapidly alters in a counterclockwise pattern during this 3-hours period.
Because the surge propagates into Lake Pontchartrain from the Gulf of Mexico via Lake
Borgne (see Figure 4.3), a huge amount of water flows into Lake Pontchartrain and the
203
magnitude of oscillation (the height of WSE) in Lake Pontchartrain evidently increases
even though the hurricane leaves the central and northeast regions of the lake.
Furthermore, the node line ( 0 = η ) disappears and the WSE in the entire lake is greater
than the reference WSE ( 0 = η ) from 07:00 pm, as it is seen from Figure 4.164.
In the final 3-hours period (from 10:00 pm UTC on August 29 to 12:00 am UTC August
30, 2005), the strength of the Route 1-traveling Hurricane Katrina with reduced forward
speeds gradually weakens from Category 3 to 2 and finally the hurricane moves inwardly
into the northeastern region of the United States of America as the original Hurricane
Katrina moves inwardly (see Figures 4.2 and 4.28). Although the direction of dominant
wind keeps turning counterclockwise during this 3-hours period, the wind generated by
the hurricane is evidently weaker than it was in the previous 21-hours period. Since the
hurricane moves away from the lake, the magnitude of oscillation in Lake Pontchartrain
drastically reduces and is much smaller than it was in the previous 3-hour period.
Besides, the major sloshing motion is moving toward the east within this 3-hours period.
The WSE in the lake significantly recede although there is not enough wind stress to
drive out the water from Lake Pontchartrain to Lake Borgne and other surrounding water
bodies (for example, Lake Maurepas); meanwhile, the WSE in the entire lake remains
greater than the reference WSE ( 0 = η ) in this 3-hours period. Besides, there is a
significant drawdown in the east portion of Lake Pontchartrain at the finale of the
numerical simulation (10:00 pm August 29 to 12:00 am August 30, 2005) as it is seen
204
from Figures 4.167 to 4.169. We can obtain these discoveries by examining the temporal
variations of WSE from Figures 4.164 to 4.169. Furthermore, the significant findings
drawn from these hourly contour maps (from Figures 4.145 to 4.169) are summarized in
the following paragraphs.
The Route 1-traveling Hurricane Katrina with reduced forward speeds moves in a nearly
north direction and passes through the regions nearby the east shore of Lake
Pontchartrain between 12:00 am UTC August 29, 2005 and 12:00 am UTC August 30,
2005 corresponding to the entire 24-hours of the numerical simulations made by the
present model. The closest encounter between the Route 1-traveling Hurricane Katrina
with reduced forward speeds and Lake Pontchartrain takes place between 03:00 pm UTC
August 29, 2005 and 12:00 am UTC August 30, 2005 (or between 10:00 am and 7:00 pm
Local Time). During this 9-hours period, there are three significant factors of the
hurricane needed to be reviewed:
1. The hurricane remains Category 3 intensity of Saffir-Simpson Scale until 21:00
pm UTC (16:00 pm Local Time), after which the strength of the hurricane
gradually reduces to Category 2.
2. The hurricane is moving in a nearly north direction with an approximate speed of
19 to 22 km/hr.
3. The distance between the eye of the hurricane and the east shore of the lake is
approximately 12 km.
205
Because of these three unique characteristics of the interaction between the hurricane and
the lake, the sloshing motion of the lake water surface changes in a counterclockwise
pattern in the lake as the hurricane itself rotates in the counterclockwise character. In
detail, the dominant sloshing motion at Lake Pontchartrain turns from the southwest to
the east within this 9-hours period. During this 9-hours, the highest amplitude of
oscillation (maximum WSE) along the south shore of the lake happens around 06:00 pm
UTC (1:00 pm Local Time) with a magnitude of 4.33 m to 4.45 m predicted by the
present model
Furthermore, the moving direction of the storm surge gradually changes from the west
direction to the east direction within the entire 24-hours period (12:00 am UTC August
29, 2005 to 12:00 am UTC August 30, 2005) of the numerical simulations (see Figures
4.145 to 169); in other words, the sloshing motion slowly changes
o
180 in 24 hours.
Therefore, the oscillation (rise and fall of water level) in a semi-enclosed lake induced by
a hurricane will be moving around the lake in a counterclockwise-turning pattern
whenever a hurricane passes through the regions surrounding the east shore of the lake.
While a hurricane circulates counterclockwise and the direction of the accompanying
wind generated by the hurricane turns in a counterclockwise pattern, the magnitude of
oscillation thoroughly depends on the strength (wind speed) and the duration (length in
time) of the wind to a specific direction. In other words, the magnitude of the oscillation
(height of rise and fall) associated with the moving direction will be different at each
specific location around the lake.
206
4.6 Risk-Based Design and Analysis
The concept of risk-based design and analysis has been known for many years. The basic
concept of risk-based design is schematically shown on Figure 4.170. The risk function
accounting for the uncertainties of various factors can be obtained by using the reliability
computation procedures. Alternatively, the risk function can account for the potential
undesired disaster associated with the failure of hydraulic structures.
Risk costs associated with the failure of hydraulic structure can not be precisely estimated
year by year. It is a practical way to quantify it by using an expected cost on the annual
basis. The total annual expected cost (TAEC) is the sum of the annual installation cost
and annual expected damage cost and TAEC can be mathematically expressed as
DC CRF IC TAEC + ∗ = (4.1)
where IC is the total installation costs that is determined by the size and configuration of
the hydraulic structure; DC is the annual expected damage cost associated with the
system failure; and CRF is the capital recovery factor, which leads the present worth of
the installation costs to an annual basis, expressed by
207
( )
( )
T
T
i i
i
CRF
+
− +
=
1
1 1
(4.2)
with T and i being the expected service life of the system and the interest rate,
respectively.
Project Size
A n n u a l C o s t
Annual Expected Damage Cost
Annual Installation Cost
Annual Total E xpected Cost
Figure 4.170 Schematic Diagram of Risk-Based Design
As the size of the hydraulic structure increases, the annual installation cost increases
while the annual expected damage cost associated with the system failure decreases. The
lowest point of the total annual expected cost curve will be used to determine the optimal
risk-based design size of the hydraulic structure.
208
The major application of the present model is to assist the design of the water-front
structure surrounding the semi-enclosed water body that has been tremendously
influenced by the oscillations induced by hurricanes. Accompanying with the historical
records of the paths and strengths of hurricanes which have brought the catastrophic
damages to the surrounding communities of the bays, lakes, and harbors, the oscillation
phenomena induced by the hurricanes will be fully understood. Therefore, the numerical
simulations generated by the present model based on the meteorological inputs can help
the planners to determine the optimal size of the hydraulic structures protecting the
surrounding communities of the semi-enclosed water body.
209
Chapter 5: Conclusions
The major objective of this research has been to study the oscillations (storm surges) of
the semi-enclosed water body induced by hurricanes. A finite-volume method (FVM)
model is developed to solve the depth-averaged, non-linear shallow-water equations
(NLSW). The present model is used to investigate the oscillations in Lake Pontchartrain
induced by wind generated by the four (4) synthetic hurricanes, including Hurricane
Katrina, between 00:00 UTC August 29, 2005 and 00:00 UTC August 30, 2005. The
available meteorological data of Hurricane Katrina is used to re-generate the hurricane
for the present model and the available measured data of the water levels in Lake
Pontchartrain is used to verify the simulated water surface elevations (WSE’s) obtained
from the present model.
5.1 Summary of Model Verification
The comparison between the measured hydrograph and the predicted hydrograph
obtained from the present model at each one of the following eight (8) sites: the 17
th
Street Canal, the Orleans Avenue Canal, the London Avenue Canal, the IHNC-Lakefront
Airport, Midlake, Bayou Labranch, Pass Manchac, and Little Irish Bayou shows:
1. The general trends of the rise and fall of water level are correctly predicted at the
17
th
Street Canal, the Orleans Avenue Canal, the London Avenue Canal, the
210
IHNC-Lakefront Airport, and the Midlake sites by the present model when they
are compared with the general trends of the rise and fall of water level showing on
the available field data at these five (5) sites.
2. The differences of the maximum water surface elevation (WSE) between the
predicted hydrographs obtained from the present model and the field observatory
hydrographs measured at these four (4) sites along the south shore of Lake
Pontchartrain, the 17
th
Street, the Orleans Avenue and the London Avenue
Canals, and the IHNC-Lakefront Airport are within the range of 0.01 to 0.36
meter (or 0.3% ~ 10%).
3. As presented in Figures 4.7 and 4.13, the Bayou La Branche site is not within the
general boundary of Lake Pontchartrain. Besides, the Bayou La Branche gage
(NOAA Station ID: 8762372) is connected to Lake Pontchartrain by a channel
which is about 0.5 mile along. Therefore, the low water surface elevations
recorded by the gage are due to the geographic characteristics of the gage
location. However, the general trend of the water level is reasonably predicted by
the present model when the computed hydrograph is compared with the observed
hydrograph; in addition, the difference of the maximum water surface elevation
(WSE) between the predicted magnitude made by the present model and the
estimated magnitude demonstrated by IPET is within the range of 0.5 to 0.6 meter
(or 20% ~ 25%) at the Bayou La Branche site.
4. As presented in Figures 4.7 and 4.13, the Pass Manchac site is located outside the
general boundary of Lake Pontchartrain. Thus, the current computations do not
211
accommodate the geographic and hydraulic complexities among the Pass
Manchac area. However, the general trend of the water level is reasonably
predicted by the present model when the computed hydrograph is compared with
the observed hydrograph at the Pass Manchac site.
5. The storm surges intruding from Gulf of Mexico through the swamps along Lake
Pontchartrain are not included in the present model. According to the IPET
report, the majority of the swamps along the east shore of Lake Pontchartrain has
been inundated by the storm surges from Gulf of Mexico before the start of the
numerical simulations (12:00 am August 29, 2005). Hence, the water surface
elevation (WSE) at Gulf of Mexico via Lake Borgne and Lake St. Catherine can
significantly affect the rise and fall of the water level at the east part of Lake
Pontchartrain. However, the present model still reasonably predicts the general
trend of the rise and fall of the water level when the computed hydrograph is
compared with the observed hydrograph at Little Irish Bayou site.
Based on these five (5) observed results, the present model has been verified to be a
reliable tool to study the oscillations of semi-enclosed water body induced by hurricanes.
Both the predicted hydrographs and the predicted hourly contour maps showing the water
surface elevation (WSE) of Lake Pontchartrain obtained from the present model provide
valuable information in studying the oscillations of a semi-enclosed lake induced by
hurricanes.
212
5.2 Major Findings from Applications of the Present Model to
Synthetic Hurricanes
The major conclusions drawn from the hydrographs and the hourly contour maps
showing the oscillations of Lake Pontchartrain induced by the winds generated by the
four (4) synthetic hurricanes and the accompanying meteorological characteristics of
these four (4) hurricanes are summarized in the following sub-sections.
5.2.1 Synthetic Hurricane No. 1
The first synthetic hurricane assumes Hurrcane Katrina tracking on its original route. All
meteorological parameters of this synthetic hurricane are identical to Hurricane Katrina,
including the forward moving track. This synthetic hurricane moves in a nearly north
direction and passes through the regions close to the east shore of Lake Pontchartrain
between 12:00 am and 06:00 pm UTC August 29, 2005 corresponding to the first 18-
hours of the numerical simulations made by the present model. Because of these two
characteristics of the interaction between the hurricane and the lake, the sloshing motion
of the lake water surface rotates in a counterclockwise pattern as the hurricane circulates
counterclockwise. The closest encounter between Hurricane Katrina and Lake
Pontchartrain takes place between 12:00 and 06:00 pm UTC (or 7:00 am and 1:00 pm
Local Time) August 29, 2005. During this 6-hours period, the highest amplitude of
213
oscillation (maximum WSE) along the south shore of the lake happens around 03:00 pm
UTC (10:00 am Local Time) with a magnitude of 3.27 m to 3.30 m predicted by the
present model while the highest water level, reported in IPET report, associated with the
time is within the range of 10.8 ft to 12.0 ft (or 3.29 m to 3.66 m) along the south shore of
Lake Pontchartrain. Based on the IPET report, the majority of floods caused by the storm
surge induced by Hurricane Katrina in the highly-populated communities along the south
shore of Lake Pontchartrain took place within this 6-hours period. Consequently, these
floods created the severe human loss and property damages in these communities.
The moving direction of the storm surge changes from the west direction to the east
direction during the first 16-hours period of the numerical simulations (the sloshing
motion changes
o
180 in 16 hours). Therefore, the oscillation (rise and fall of water level)
in a semi-enclosed lake induced by a hurricane will be moving around the lake in a
counterclockwise-turning pattern. Meanwhile, the magnitude of the oscillation (height of
rise and fall) associated with the moving direction will be different at each specific
location around the lake.
Since the major communities, i.e. New Orleans, of business importance, dense population
and historical heritage, are located within the region along the south shore of Lake
Pontchartrain, a natural disaster of a catastrophic scale will have impact of national
significance. When the eye of Hurricane Katrina is passing through the region along the
east shore of Lake Pontchartrain, the highest amplitude (maximum WSE) of oscillation
214
along the south shore of Lake Pontchartrain takes place at the time at which the sloshing
motion in the lake is moving toward the south, directly intruding into the region along the
south shore of the lake. Consequently, the major floods caused by these large oscillations
induced by Hurricane Katrina within a short period of time along the south shore of Lake
Pontchartrain create a catastrophe with enormous impacts to the city of New Orleans
even though the city is protected by the hurricane protection systems built under the Lake
Pontchartrain and Vicinity project (one of the three major projects under a comprehensive
hurricane protection plan for New Orleans and the Southeast Louisiana region).
5.2.2 Synthetic Hurricane No. 2
The second synthetic hurricane assumes Hurrcane Katrina tracking 36 km west of its
original route. All other meteorological components of this synthetic hurricane are
identical to Hurricane Katrina, except the forward moving track. This synthetic hurricane
moves in a nearly north direction and passes through the east part of New Orleans,
Louisiana and both the east and central parts of Lake Pontchartrain between 12:00 am
and 06:00 pm UTC August 29, 2005 corresponding to the first 18-hours of the numerical
simulations made by the present model. Due to these two characteristics of the
interaction between the hurricane and the lake, the sloshing motion at Lake Pontchartrain
rotates in a counterclockwise pattern as the hurricane circulates counterclockwise. The
closest encounter between this synthetic hurricane and Lake Pontchartrain takes place
between 12:00 and 06:00 pm UTC August 29, 2005. During this 6-hours period, the
215
highest amplitude of oscillation (maximum WSE) along the south shore of Lake
Pontchartrain will occur around 03:00 pm UTC with a magnitude of 3.53 m to 3.86 m as
predicted by the present model.
The moving direction of the storm surge changes from the west direction to the east
direction during the first 16-hours of the numerical simulations (the sloshing motion
changes
o
180 in 16 hours). Therefore, the oscillation (rise and fall of water level) in a
semi-enclosed lake induced by a hurricane will be moving around the lake in a
counterclockwise-turning pattern. Meanwhile, the magnitude of the oscillation (height of
rise and fall) associated with the moving direction will be different at each specific
location around the lake.
5.2.3 Synthetic Hurricane No. 3
The third synthetic hurricane assumes Hurrcane Katrina tracking 72 km west of its
original route. All other meteorological parameters of this synthetic hurricane are
identical to Hurricane Katrina, except the forward moving track. This synthetic hurricane
moves in a nearly north direction and passes over the west shore and its surrounding
regions of Lake Pontchartrain between 12:00 am and 06:00 pm UTC August 29, 2005
corresponding to the first 18-hours of the numerical simulations made by the present
model. Due to these two characteristics of the interaction between the hurricane and the
216
lake, the sloshing motion at Lake Pontchartrain rotates in a clockwise pattern even though
the hurricane circulates counterclockwise. The closest encounter between this synthetic
hurricane and Lake Pontchartrain takes place between 12:00 and 06:00 pm UTC August
29, 2005. During this 6-hours period, both the lowest and the highest amplitudes of
oscillation (or minimum and maximum WSE’s) along the south shore of Lake
Pontchartrain will occur around 03:00 pm UTC with the highest magnitude of 3.11 m to
3.33 m as predicted by the present model.
The moving direction of the storm surge changes from the west direction to the east
direction during the first 16-hours of the numerical simulations (the sloshing motion
changes
o
180 in 16 hours). Therefore, the oscillation (rise and fall of water level) in a
semi-enclosed lake induced by a hurricane can be moving around the lake in a clockwise-
turning pattern whenever a hurricane passes through regions surrounding the west shore
of the lake. Meanwhile, the magnitude of the oscillation (height of rise and fall)
associated with the moving direction will be different at each specific location around the
lake.
5.2.4 Synthetic Hurricane No. 4
The fourth synthetic hurricane assumes Hurrcane Katrina tracking on its original route
but with reduced forward speeds; hence, two major meteorological parameters of this
217
synthetic hurricane, central pressures and radii of maximum winds, are obtained by
modifying the observatory data of Hurricane Katrina. This synthetic hurricane moves in
a nearly north direction and passes through the regions nearby the east shore of Lake
Pontchartrain between 12:00 am UTC August 29, 2005 and 12:00 am UTC August 30,
2005 corresponding to the entire 24-hours of the numerical simulations made by the
present model. Because of these two characteristics of the interaction between the
hurricane and the lake, the sloshing motion at Lake Pontchartrain rotates in a
counterclockwise pattern as the hurricane circulates counterclockwise. The closest
encounter between this synthetic hurricane and Lake Pontchartrain takes place between
03:00 pm UTC August 29, 2005 and 12:00 am UTC August 30, 2005. During this 9-
hours period, the highest amplitude of oscillation (maximum WSE) along the south shore
of Lake Pontchartrain will happen around 06:00 pm UTC with a magnitude of 4.33 m to
4.45 m predicted by the present model. Evidently, the maximum water surface elevations
(WSE’s) along the south shore of Lake Pontchartrain induced the wind generated by this
synthetic hurricane (Hurricane Katrina tracking on its original route with reduced forward
speeds) will be 1 m higher than the ones induced by the wind generated by the genuine
Hurricane Katrina. Thus, should this condition occur, the floods and the accompanying
catastrophes caused by this synthetic hurricane would be much severe than the ones
caused by Hurricane Katrina.
The moving direction of the storm surge changes from the west direction to the east
direction during the entire 24-hours of the numerical simulations (the sloshing motion
218
slowly changes
o
180 in 24 hours). Therefore, the oscillation (rise and fall of water level)
in a semi-enclosed lake induced by a hurricane would still be moving around the lake in a
counterclockwise-turning pattern if the hurricane would pass over the regions nearby or
surrounding the east shore of the lake. Meanwhile, the magnitude of the oscillation
(height of rise and fall) associated with the moving direction will be different at each
specific location around the lake.
219
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Abstract (if available)
Abstract
A numerical study is conducted to simulate the oscillations (storm surges) of semi-enclosed water body induced by hurricanes. For application using the numerical model developed in the present study, Lake Pontchartrain (located in southeastern Louisiana) is chosen as the semi-enclosed water body and Hurricane Katrina (the costliest hurricane in the history of the United States) is chosen as the hurricane. There are three (3) reasons to choose Lake Pontcharrain and Hurricane Katrina: 1. Storm surge built up in Lake Pontchartrain during Hurricane Katrina, 2. Wind drove water into Lake Pontchartrain as Hurricane Katrina approached from the Gulf of Mexico, and 3. The extensive field data, gathered by the Interagency Performance Evaluation Task Force (IPET), is available to provide the needed comparison of numerical result and prototype data on the oscillations at Lake Pontchartrain induced by Hurricane Katrina.
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University of Southern California Dissertations and Theses
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Asset Metadata
Creator
Tan, Yuan-Hung Paul
(author)
Core Title
Oscillations of semi-enclosed water body induced by hurricanes
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Civil Engineering
Publication Date
10/19/2010
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
depth-averaged,finite-volume method (FVM),Hurricane Katrina,Lake Pontchartrain,non-linear shallow water eqautions (NLSW),OAI-PMH Harvest,oscillations,risk-based design and analysis
Place Name
lakes: Lake Pontchartrain
(geographic subject),
Louisiana
(states)
Language
English
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Electronically uploaded by the author
(provenance)
Advisor
Lee, Jiin-Jen (
committee chair
), Lee, Vincent W. (
committee member
), Moore, James Elliott, II (
committee member
), Nasseri, Iraj (
committee member
), Wellford, L. Carter (
committee member
)
Creator Email
yctan@earthlink.net,yuanhtan@usc.edu
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-m3506
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UC188527
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etd-Tan-4151 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-423429 (legacy record id),usctheses-m3506 (legacy record id)
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423429
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Tan, Yuan-Hung Paul
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(contributing entity),
University of Southern California Dissertations and Theses
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Repository Location
Los Angeles, California
Repository Email
cisadmin@lib.usc.edu
Tags
depth-averaged
finite-volume method (FVM)
Hurricane Katrina
Lake Pontchartrain
non-linear shallow water eqautions (NLSW)
oscillations
risk-based design and analysis