Boussinesq systems in two space dimensions over a variable bottom for the generation and propagation of tsunami waves

TL;DR

This paper develops and numerically solves a simplified Boussinesq system for modeling tsunami wave generation and propagation over variable bottoms, comparing results with analytical solutions and real event data.

Contribution

It introduces a simplified Boussinesq model for tsunamis over variable bottoms and validates it through numerical simulations against analytical solutions and real-world data.

Findings

The simplified Boussinesq system accurately models tsunami generation and propagation.

Numerical results agree well with analytical solutions of linearized Euler equations.

The model effectively simulates the Java 2006 tsunami event.

Abstract

Considered here are Boussinesq systems of equations of surface water wave theory over a variable bottom. A simplified such Boussinesq system is derived and solved numerically by the standard Galerkin-finite element method. We study by numerical means the generation of tsunami waves due to bottom deformation and we compare the results with analytical solutions of the linearized Euler equations. Moreover, we study tsunami wave propagation in the case of the Java 2006 event, comparing the results of the Boussinesq model with those produced by the finite difference code MOST, that solves the shallow water wave equations.