In this talk, we are interested in the asymptotic dynamics of a fast rotating incompressible fluid in the regime of vanishing Rossby number. We assume that the fluid moves in a three-dimensional domain with topography (including the possible presence of a land area) and we impose no-slip conditions at the boundary. By proving a "weak implies strong" convergence principle and constructing Ekman layers adapted to the geometry of the domain, we characterise the limit velocity profile and show that it evolves following a linear dynamics.

The talk is based on a joint work with J.-Y. Chemin (Université Claude Bernard Lyon 1) and I. Gallagher (École Normale Supérieure - Paris).