TY - JOUR
T1 - A mathematical analysis of tsunami generation in shallow water due to seabed deformation
AU - Iguchi, Tatsuo
PY - 2011/6
Y1 - 2011/6
N2 - In numerical computations of tsunamis due to submarine earthquakes, it is frequently assumed that the initial displacement of the water surface is equal to the permanent shift of the seabed and that the initial velocity field is equal to zero and the shallow-water equations are often used to simulate the propagation of tsunamis. We give a mathematically rigorous justification of this tsunami model starting from the full water-wave problem by comparing the solution of the full problem with that of the tsunami model. We also show that, in some cases, we have to impose a non-zero initial velocity field, which arises as a nonlinear effect.
AB - In numerical computations of tsunamis due to submarine earthquakes, it is frequently assumed that the initial displacement of the water surface is equal to the permanent shift of the seabed and that the initial velocity field is equal to zero and the shallow-water equations are often used to simulate the propagation of tsunamis. We give a mathematically rigorous justification of this tsunami model starting from the full water-wave problem by comparing the solution of the full problem with that of the tsunami model. We also show that, in some cases, we have to impose a non-zero initial velocity field, which arises as a nonlinear effect.
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U2 - 10.1017/S0308210509001279
DO - 10.1017/S0308210509001279
M3 - Article
AN - SCOPUS:79958783205
SN - 0308-2105
VL - 141
SP - 551
EP - 608
JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics
JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics
IS - 3
ER -