Mercredi 22 janvier à 16h30 ; salles des séminaires IRPHE
Accurately predicting the complex dynamics of ocean waves is fundamental to advancing our understanding of the marine environment. In this talk, I will present my work on two important classes of ocean waves: free-surface waves and continuously stratified internal waves.
In the first part of the talk, I will focus on free-surface gravity waves governed by the Euler equations under the assumption of irrotational flow. The development of model equations for these waves is an ongoing effort aimed at enabling simulations over extended spatial domains, longer time scales, and with higher fidelity in representing physical processes. These models replace the original free-boundary hydrodynamic problem with numerically simpler formulations that retain the essential physics. I will describe two modeling strategies to derive model equations from the variational principle of the original problem utilizing series representations of the velocity potential. The first approach uses an enhanced eigenfunction expansion inspired by linear wave theory while the second one uses a polynomial representation inspired by long-wave theory. For the second approach, I will explore the connections between with asymptotic models, and present numerical solutions capturing strongly nonlinear and dispersive wave behavior.