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

Juliette Dubois (1) , Sébastien Imperiale (2, 3) , Anne Mangeney (4) , Jacques Sainte-Marie (5, 4)

1 RWTH - Rheinisch-Westfälische Technische Hochschule Aachen University
2 M3DISIM - Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine
3 LMS - Laboratoire de mécanique des solides
4 ANGE - Numerical Analysis, Geophysics and Ecology
5 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

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.

Keywords: Hydro-acoustic waves; Tsunami; Spectral element method; Linearized Euler equation

Domains: Analysis of PDEs [math.AP]; Geophysics [physics.geo-ph]

Juliette Dubois, Sébastien Imperiale, Anne Mangeney, Jacques Sainte-Marie. Well-posedness and potential-based formulation for the propagation of hydro-acoustic waves and tsunamis. 2024. ⟨hal-04558414⟩