A mathematical model for Tsunami generation using a conservative velocity-pressure hyperbolic system

TL;DR

This paper introduces a conservative hyperbolic velocity-pressure model for tsunami generation, incorporating gravity and friction, and analyzes how seismic waves evolve into potentially tsunami-forming surface waves.

Contribution

It develops a novel velocity-pressure hyperbolic system based on detonics principles, extending Euler equations with a strain-dependent density and non-homogeneous terms.

Findings

Pressure wave amplitude diminishes before reaching the surface

Strong tremors can produce residual waves capable of forming tsunamis

Model describes wave profile evolution and conditions for tsunami formation

Abstract

By using the Hugoniot curve in detonics as a Riemann invariant of a velocity-pressure model, we get a conservative hyperbolic system similar to the Euler equations. The only differences are the larger value of the adiabatic constant (= 8.678 instead of 1.4 for gas dynamics) and the mass density replaced by a strain density depending on the pressure. The model is not homogeneous since it involves a gravity and a friction term. After the seismic wave reaches up the bottom of the ocean, one gets a pressure wave propagating toward the surface, which is made of a frontal shock wave followed by a regular decreasing profile. Since this regular profile propagates faster than the frontal shock waves, the amplitude of the pressure wave is strongly reduced when reaching the surface. Only in the case of a strong earth tremor the residual pressure wave is still sufficient to generate a water elevation with a sufficient wavelengths enable to propagate as a SaintVenant water wave and to become a tsunami when reaching the shore. We describe the construction of the model and the computation of the wave profile and discuss about the formation or not of a wave.