Highly rotating fluids in rough domains |
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Institution: | UMPA, UMR 5669, ENS Lyon, 46 Allée d''Italie, 69364 Lyon, France |
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Abstract: | 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 strong convergence theorem on solutions of Navier–Stokes–Coriolis equations, as ε goes to 0, 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 give a substantial refinement of the results obtained on flat boundaries with the classical Ekman layers. |
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