Viscous Fluid Flow over a Corrugated Bottom in a Strongly Rotating System

The problem of a laterally unbounded viscous flow across slight bottom corrugations at a right angle in a strongly rotating system is considered. It is shown that when the ratio of the Rossby number to the Reynolds number δ2 ≡ Ro/Re ≪ 1 and Re = δ−m, m < 1, the flow far away from the bottom is both geostrophic and hydrostatic to a high degree and that flow near the bottom is of the boundary-layer type with negligible inertia. A steady-state solution for the entire flow field is obtained in which boundary-layer suction maintains the mass continuity as fluid is pushed across the uneven bottom at a constant speed. Experimental results for a bottom of constant slope are presented which are in good agreement with theory.