Convergence of the rotating fluids system in a domain with rough boundaries

Gérard-Varet, David

Journées équations aux dérivées partielles (2003), article no. 8, 15 p.

We consider a rotating fluid in a domain with rough horizontal boundaries. The Rossby number, kinematic viscosity and roughness are supposed of characteristic size $ϵ$. We prove a convergence theorem on solutions of Navier-Stokes Coriolis equations, as $ϵ$ goes to zero, in the well prepared case. We show in particular that the limit system is a two-dimensional Euler equation with a nonlinear damping term due to boundary layers. We thus generalize the results obtained on flat boundaries with the classical Ekman layers.

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