Well-posedness and potential-based formulation for the propagation of hydro-acoustic waves and tsunamis

TL;DR

This paper introduces a new potential-based formulation for modeling hydro-acoustic waves and tsunamis in stratified oceans, simplifying mathematical analysis and improving discretization efficiency.

Contribution

It develops a novel formulation based on functional analysis, proving well-posedness and linking it to previous models, with applications to tsunami simulation.

Findings

Both formulations are well-posed.

The new formulation simplifies analysis and discretization.

Simulations of tsunami generation demonstrate practical effectiveness.

Abstract

We study a linear model for the propagation of hydro-acoustic waves and tsunami in a stratified free-surface ocean. A formulation was previously obtained by linearizing the compressible Euler equations. The new formulation is obtained by studying the functional spaces and operators associated to the model. The mathematical study of this new formulation is easier and the discretization is also more efficient than for the previous formulation. We prove that both formulations are well posed and show that the solution to the first formulation can be obtained from the solution to the second. Finally, the formulations are discretized using a spectral element method, and we simulate tsunamis generation from submarine earthquakes and landslides.