The sharp stratification limit: from continuous to bilayer models for a stratified ocean

In the study of oceanic flows at the geophysical scale, the phenomenon of density stratification plays a central role in the dynamics of the system. Two categories of mathematical models are commonly used to describe the role played by the density stratification: on the one hand, continuously stratified models - such as the stratified Euler equations in a strip, considered in this talk - offer an accurate description of vertical effects, but come with a high level of complexity, both at the theoretical and numerical levels. On the other hand, bilayer models approximate the stratification by a piecewise constant profile. In the latter case, the main point is to study the evolution of the free interface between both layers, which leads to a substantially simplified model. During this talk, we will compare both approaches in the framework of the linearized stratified Euler equations around density profiles that are close to piecewise constant profiles, and prove the convergence towards the bilayer Euler equations. If time allows, we will study the effect of a shear flow, which is an intermediate step between the previous study and the non-linear model, through a numerical approach.