Geoscience Reference
In-Depth Information
Chapter 5
Propagation of a Tsunami in the Ocean
and Its Interaction with the Coast
Abstract Traditional ideas of tsunami propagation in the open ocean are dealt with.
The significance is estimated of manifestations of phase and amplitude dispersions.
Classical problems are considered, concerning variation of the amplitude of a long
wave in a basin with gently varying depth (Green's law) and the reflection of a
wave from a step and from a rectangular obstacle. Formulae of the ray method are
presented in Cartesian and spherical coordinate systems. Phenomena of long-wave
refraction and capture by underwater ridges and the shelf are described. Estima-
tion is performed of linear (viscous) and non-linear (turbulent) dissipation of the
energy of long waves. The effect of a wave amplitude being reduced by scattering
on bottom irregularities is considered. Approaches to the numerical simulation of
tsunami wave propagation are described. Conventionally applied equations of non-
linear long-wave theory, taking into account the Coriolis force and bottom friction,
are presented both in Cartesian and spherical coordinate systems. The technique for
formulating initial and boundary conditions in the tsunami propagation problem is
described. Brief information is given on certain tsunami models (codes) that are ac-
tively applied at present. Features of transoceanic wave propagation are considered,
taking advantage of the 26 December 2004 tsunami as an example. The main results,
due to investigation of the issues of a tsunami run-up on the shore, are presented.
Keywords Tsunami propagation
tsunami run-up
phase dispersion
amplitude
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dispersion
long-wave theory
Green's law
refraction
reflection
scattering
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dissipation
numerical tsunami models
non-linear long-wave theory
bottom fric-
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tion
Coriolis force
Manning coefficient
Cartesian reference system
spherical
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coordinates
initial elevation
boundary conditions
bathymetry
topography
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waveguide
ridge
breaking waves
run-up height
laboratory experiments
nu-
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merical simulations
We have already noted that the following three stages are traditionally distinguished
in the life of a tsunami: generation of the wave, its propagation in open ocean
and its interaction with the coast (its uprush or run-up). The most simple task
is to describe tsunami propagation in the open ocean. In this case, the wave's
