In this talk we present a new linear model for the propagation of acoustic waves and gravity waves in a simplified ocean. The use of acoustic waves measurements in the ocean is currently seen as a good candidate for the improvement of tsunami early-warning systems. The new model is obtained in the following way: the compressible Euler equation are written in Lagrangian coordinates and linearized around a state at equilibrium corresponding to the ocean at rest. A wave-like equation containing acoustic terms and gravity terms is then derived. The obtained model is compared with the literature by using some simplifications, namely the barotropic assumption, and the limits in the incompressible and in the acoustic regime.
We present then some numerical results. By using a finite element discretization in space and a finite difference scheme in time, we are able to reproduce the simulations available in the literature for the case without topography and with a constant temperature. Finally we show some aspects of the mathematical analysis for the continuous problem, and focus on the functional space needed to prove existence and uniqueness of the solution.
This is a joint work with Jacques Sainte-Maris (Inria Paris, ANGE) and Sébastien Imperiale (Inria Saclay, M3DISIM).