Geoscience Reference
In-Depth Information
translates to the water-surface displacement. This requires advancing the understanding of
the source and its rupture mechanisms given the current uncertainties around many of the
potential sources. In addition to the source parameters, there is inherent uncertainty in the
models and the accuracy of topographic and bathymetric data that precludes the possibility of
a completely accurate and precise tsunami inundation model. It is multi-scale because of differ-
of differ-
ences in the wavelength of tsunamis (on the order of hundreds of kilometers) and the effects
It is multi-scale because of differ-
e because of differ-
of differ-
effects
of their inundation (to be described at scales of a few meters or less), and as such, numerical
the order of hundreds of kilometers) and the effects
) and the effects
), and as such, numerical
simulations must use nested or adapted grids (e.g., large grids for the propagation across the
abyssal plain, smaller grids across the continental shelf, and the smallest grids for onshore
run-up motions). The current state of knowledge regarding hydrodynamic modeling at various
stages of tsunami propagation is discussed in the following section.
Tsunami propagation is usually computed based on the shallow water wave theory. The
theory comprises conservations of luid volume and linear momentum with the assump-
tions of hydrostatic pressure ield, uniform horizontal velocities over depth, and water being
incompressible. The shallow water wave theory can be justiied because tsunamis from a
seismic source are very long and the depth of ocean is relatively shallow (on the order of 4
km). Although tsunamis contain a wide range of spectral components at the source, most of
the energy is contained in the long wave components, and shorter-length (higher frequency)
waves are soon left behind and disperse. For tsunami propagation in the open ocean, the
nonlinearity effect may be insigniicant because the wave amplitude (less than a few meters)
is much smaller than the depth; hence the linear shallow water wave theory with large spatial
grid size (but less than 1 minute = 2 km) may be adequate for the propagation computations
(Scientiic Committee on Oceanic Research, 2001). Given that the actual resolution of the
sealoor data is generally much poorer than 2 km, however, the impact of potential, realistic
variability (e.g., assuming bathymetry obeys a power law) should be studied.
When the tsunami reaches the continental slope, a portion of incident tsunami energy
could relect back to the ocean, depending on the abruptness of the depth change. For the
tsunami that travels onto the continental shelf, the amplitude will increase due to the shoaling
effect; hence, the nonlinearity effect (i.e., measured by the ratio of wave amplitude to the depth)
increases. At the same time, the dispersion effect (i.e., measured by the ratio of water depth to
the wave length) could become important depending on the length of the incoming tsunami
and the width of the continental shelf. When the continental shelf is suficiently wide in com-
parison to the tsunami wavelength, a single pulse of the incoming tsunami could be trans-
formed to a series of shorter waves. This phenomenon is often called “ission” (Madsen and Mei,
1969) when the incident wave is speciically a solitary wave—a stable permanent-form wave in
their inundation (to be described at scales of a few meters or less), and as such, numerical
inundation (to be described at scales of a few meters or less), and as such, numerical
(to be described at scales of a few meters or less), and as such, numerical
scales of a few meters or less), and as such, numerical
stable permanent-form wave in
shallow water. Although co-seismically generated tsunamis do not evolve to the “exact” form of
a stable permanent-form wave in
stable permanent-form wave in
. Although co-seismically generated tsunamis do not evolve to the “exact” form of
solitary waves because of the insuficient distance to evolve in any oceans (Hammack and Segur,
1978), it is anticipated that the ission-like phenomenon must take place. When the width of the
continental shelf is much smaller than the incoming tsunami wavelength, the intruding tsunami
does not have suficient time to split itself into a series of shorter waves; hence the tsunami
could reach shore without signiicant dispersion. In the former case (i.e., dispersion effects are
important), the model based on the Boussinesq approximation (weakly nonlinear and weakly
