A mathematical analysis of tsunami generation in shallow water due to seabed deformation

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Abstract

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.

Original languageEnglish
Pages (from-to)551-608
Number of pages58
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume141
Issue number3
DOIs
Publication statusPublished - 2011 Jun

Fingerprint

Tsunami
Shallow Water
Mathematical Analysis
Velocity Field
Shallow Water Equations
Water Waves
Nonlinear Effects
Earthquake
Justification
Numerical Computation
Propagation
Water
Zero
Model

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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