Appears in collection : Nonlinear and stochastic methods in climate and geophysical fluid dynamics

The purpose of this talk is to introduce some mathematical techniques to study boundary layer systems and to apply these techniques to classical oceanographic models (Ekman and Munk boundary layers, internal layers in stratified fluids…) Note that we will tackle both the construction of the boundary layer and the proof of its validity.

I will also insist on the limitations of these techniques, and on some future challenges and open problems.