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Highly rotating fluids in rough domains. (English) Zbl 1033.76008
Summary: We consider a rotating fluid in a domain with rough horizontal boundaries. The Rossby number, kinematic viscosity and roughness are supposed to be of characteristic size \(\varepsilon\). We prove a strong convergence theorem for solutions of Navier-Stokes-Coriolis equations, as \(\varepsilon\) goes to 0, in the well-prepared case. We show, in particular, that the limit system contains 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 classical Ekman layers.

MSC:
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76U05 General theory of rotating fluids
35Q30 Navier-Stokes equations
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