Appears in collection : 2019 - T3 - WS1 - Nonlinear and stochastic methods in climate and geophysical fluid dynamics

We consider here a continuously stratified fluid and consider the propagation of internal waves. At first order, perturbations of the hydrostatic equilibrium decompose into several normal modes travelling at different speeds provided by the eigenvalues of a Sturm-Liouville problem associated to the underlying stratification. For larger times, dispersive and nonlinear effects have to be considered and complicate the analysis since the evolutions of the different modes are then coupled. We propose an asymptotic description of this coupling. 

This is a joint work with B. Desjardins and J.-C. Saut.