The separation of flow past a circular cylinder on aβ-plane

Abstract

Effects of the Ekman friction on the prograde (eastward) flows past a cylinder on aΒ-plane are investigated when$\hat \beta$ (=ΒR ²/U, whereR is the cylinder radius andU the freestream speed)∼O(1) andα(=2E _k ^1/2/R ₀·δ∼O(1) where$\hat \beta$ is the non-dimensional beta parameter andα the ratio of the square root of the Ekman numberE _k multiplied by 2 to the Rossby numberRo multiplied by the aspect ratioδ(=H/R, whereH is the fluid depth). Previous studies without the Ekman friction have shown that theΒ-effect inhibits flow separation for pragrade flows through the asymptotic boundary condition by shifting the region of the adverse pressure gradient toward the rear stagnation point. It is found that the Ekman friction alleviates thisΒ-effect on the exterior flow. In the E_k ^1/4-boundary layer, on the other hand, Ekman friction suppresses the vorticity advection along the wall, which tends to make the boundary layer thickness thin and delay the flow separation. The Ekman friction thus affects flow separation in a complicated manner. Details of the boundary layer structures and the separation angles are described for 0.3<$\hat \beta$<4.0 and 0.1<α<1.5.