### 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 language | English |
---|---|

Pages (from-to) | 551-608 |

Number of pages | 58 |

Journal | Proceedings of the Royal Society of Edinburgh Section A: Mathematics |

Volume | 141 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2011 Jun |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**A mathematical analysis of tsunami generation in shallow water due to seabed deformation.** / Iguchi, Tatsuo.

Research output: Contribution to journal › Article

}

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.

UR - http://www.scopus.com/inward/record.url?scp=79958783205&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79958783205&partnerID=8YFLogxK

U2 - 10.1017/S0308210509001279

DO - 10.1017/S0308210509001279

M3 - Article

AN - SCOPUS:79958783205

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

SN - 0308-2105

IS - 3

ER -