Flow separation in a rotating annulus with bottom topography

Abstract

The flow in a rotating annular cylinder, of finite depth, is examined when the Rossby number Ro is O(E^½), where E is the Ekman number, and when there is a topography of height O(E^½) on the base of the container. The flow, relative to the rigid axial rotation, is forced by differential rotation of the lid and as it moves over the topography the streamlines are deflected parallel to the bottom surface. This induces O(1) velocity variations near the axial walls of the annulus to which the boundary layers there, of thickness O(E^¼), respond. For sufficiently large values of a parameter γ ∝Ro/E^½ the skin friction can vanish within these layers, with some similaritits to boundary-layer separation in a non-rotating fluid. In this study the interior flow, with horizontal viscous diffusion neglected, is calculated and used to provide a boundary condition for the, E^¼ layer flow. Once λ exceeds a finite critical value a singularity is encountered in the boundary layer corresponding to flow separation from the wall. This demonstrates that E^¼ layers in a rotating fluid, which for Ro = 0 have little direct influence on the interior flow, can modify the gross properties of the flow for non-zero Rossby numbers, a conclusion also reached by Walker & Stewartson (1972) in a different context.