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Free–surface motions are described using an additional variable, namely the wave
height at the free surface, introduced through the so–called free surface kinematic
boundary condition. The latter requires that the vertical velocity of the fluid at the free
surface equal the material derivative of the wave height. Sometimes this is described as
a condition that ensures that the particles on the free surface stay there, i.e., do not to
mix with the rest of the fluid. When the waves climb on dry land, additional conditions
are required to describe the runup and rundown.
As Liu et al. (1991) wrote, a certain approximation of the Navier–Stokes equations
known as the Shallow–WaterWave equation (SWE) models the hydrodynamic evolution
and runup of tsunamis unexpectedly well. The SWE are derived from the N–S equations,
if the latter are depth–averaged and the pressure is assumed hydrostatic. Another depth–
averaged formulation results into the Boussinesq equations, where the pressure is not
assumed hydrostatic. The latter equations are referred to as dispersive, in the sense that
they appropriately model shorter waves, than the SWE affected by frequency–dependent
propagation. Both the SWE and Boussinesq approximations are valid for long waves,
where depth averaging is a reasonable assumption. There is no further limitation on
the wave height. Wind waves produce disturbances that affect a small fraction of the
water column, and depth–averaging is not appropriate. Long waves are defined as waves
with wavelengths much longer than the local depth, typically more than twenty times.
Wind waves are generally dispersive, their phase and group velocities differ; hence,
the wave packet evolves rapidly, even across oceans of constant depth. A long wave
will maintain its overall shape over constant depth far longer than wind waves. For a
complete discussion, refer to Synolakis (2003).
MOST is a numerical model that solves the SWE equations, developed by Titov and
Synolakis (1997) and further described by Titov and Synolakis (1998) and Titov and
34
Object Description
| Title | Deterministic and probabilistic tsunami studies in California from near and farfield sources |
| Author | Uslu, Burak |
| Author email | uslu@usc.edu; burak.uslu@noaa.gov |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Civil Engineering |
| School | Viterbi School of Engineering |
| Date defended/completed | 2007-09-21 |
| Date submitted | 2008 |
| Restricted until | Unrestricted |
| Date published | 2008-10-30 |
| Advisor (committee chair) | Synolakis, Costas E. |
| Advisor (committee member) |
Bardet, Jean-Pierre Okal, Emile A. Moore, James Elliott, II |
| Abstract | California is vulnerable to tsunamis from both local and distant sources. While there is an overall awareness of the threat, tsunamis are infrequent events and few communities have a good understanding of vulnerability. To quantitatively evaluate the tsunami hazard in the State, deterministic and probabilistic methods are used to compute inundation and runup heights in selected population centers along the coast.; For the numerical modeling of tsunamis, a two dimensional finite difference propagation and runup model is used. All known near and farfield sources of relevance to California are considered. For the farfield hazard analysis, the Pacific Rim is subdivided into small segments where unit ruptures are assumed, then the transpacific propagations are calculated. The historical records from the 1952 Kamchatka, 1960 Great Chile, 1964 Great Alaska, and 1994 and 2006 Kuril Islands earthquakes are compared to modeled results. A sensitivity analysis is performed on each subduction zone segment to determine the relative effect of the source location on wave heights off the California Coast.; Here, both time-dependent and time-independent methods are used to assess the tsunami risk. In the latter, slip rates are obtained from GPS measurements of the tectonic motions and then used as a basis to estimate the return period of possible earthquakes. The return periods of tsunamis resulting from these events are combined with computed waveheight estimates to provide a total probability of exceedance of given waveheights for ports and harbors in California. The time independent method follows the practice of past studies that have used Gutenberg and Richter type relationships to assign probabilities to specific tsunami sources.; The Cascadia Subduction Zone is the biggest nearfield earthquake source and is capable of producing mega-thrust earthquake ruptures between the Gorda and North American plates and may cause extensive damage north of Cape Mendocino, to Seattle. The present analysis suggests that San Francisco Bay and Central California are most sensitive to tsunamis originating from the Alaska and Aleutians Subduction Zone (AASZ). An earthquake with a magnitude comparable to the 1964 Great Alaska Earthquake on central AASZ could result in twice the wave height as experienced in San Francisco Bay in 1964.; The probabilistic approach shows that Central California and San Francisco Bay have more frequent tsunamis from the AASZ, while Southern California can be impacted from tsunamis generated on Chile and Central American Subduction Zone as well as the AASZ. |
| Keyword | assessment; California; hazard; model; probability; tsunami |
| Geographic subject | capes: Kamchatka; islands: Kuril Islands; fault zones: Cascadia Subduction Zone |
| Geographic subject (state) | California; Alaska |
| Geographic subject (country) | Chile |
| Coverage date | 1952/2008 |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m1706 |
| Contributing entity | University of Southern California |
| Rights | Uslu, Burak |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | cisadmin@lib.usc.edu |
| Filename | etd-uslu-2434 |
| Archival file | uscthesesreloadpub_Volume40/etd-uslu-2434.pdf |
Description
| Title | Page 49 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | Free–surface motions are described using an additional variable, namely the wave height at the free surface, introduced through the so–called free surface kinematic boundary condition. The latter requires that the vertical velocity of the fluid at the free surface equal the material derivative of the wave height. Sometimes this is described as a condition that ensures that the particles on the free surface stay there, i.e., do not to mix with the rest of the fluid. When the waves climb on dry land, additional conditions are required to describe the runup and rundown. As Liu et al. (1991) wrote, a certain approximation of the Navier–Stokes equations known as the Shallow–WaterWave equation (SWE) models the hydrodynamic evolution and runup of tsunamis unexpectedly well. The SWE are derived from the N–S equations, if the latter are depth–averaged and the pressure is assumed hydrostatic. Another depth– averaged formulation results into the Boussinesq equations, where the pressure is not assumed hydrostatic. The latter equations are referred to as dispersive, in the sense that they appropriately model shorter waves, than the SWE affected by frequency–dependent propagation. Both the SWE and Boussinesq approximations are valid for long waves, where depth averaging is a reasonable assumption. There is no further limitation on the wave height. Wind waves produce disturbances that affect a small fraction of the water column, and depth–averaging is not appropriate. Long waves are defined as waves with wavelengths much longer than the local depth, typically more than twenty times. Wind waves are generally dispersive, their phase and group velocities differ; hence, the wave packet evolves rapidly, even across oceans of constant depth. A long wave will maintain its overall shape over constant depth far longer than wind waves. For a complete discussion, refer to Synolakis (2003). MOST is a numerical model that solves the SWE equations, developed by Titov and Synolakis (1997) and further described by Titov and Synolakis (1998) and Titov and 34 |
