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

¹ RWTH Aachen University, Math 111810, Templergraben 55, 52062 Aachen, Germany
² Inria, M3DISIM Team, Inria Saclay, 1 rue Honoré d’Estienne d’Orves, 91120 Palaiseau, France
³ Seismology Group, Institut de Physique du Globe de Paris, Université Paris Diderot, Sorbonne Paris Cité, 1 rue Jussieu, 75005 Paris, France
⁴ Inria, ANGE team, Inria Paris, 2 rue Simone Iff, 75012 Paris, France
⁵ Laboratoire Jacques-Louis Lions, Sorbonne Université, 75005 Paris, France

^* Corresponding author: dubois@eddy.rwth-aachen.de

Received: 24 April 2024
Accepted: 21 October 2024

Abstract

We study a linear model for the propagation of acoustic and surface gravity waves in a stratified free-surface ocean. A formulation was previously obtained by linearizing the compressible Euler equations. In this paper, we introduce a new formulation written with a generalized potential. 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.