The low Rossby number flow of a rotating fluid past a flat plate

Abstract

In a rotating fluid, the flow between two infinite plates, perpendicular to the rotation axis, is examined when a uniform stream is aligned with a finite flat plate, parallel to the rotation axis. Since the flow in this configuration is depth-independent the motion is analogous to that considered by Blasius in a non-rotating fluid. When the Rossby number Ro is much smaller than E3/4, where E is the Ekman number, the equations are linear and the flow has been examined by Hocking [5]. However, when Ro≫E3/4 inertial effects are important in the E1/4-layer and the boundary-layer equations are non-linear. For Ro of order E1/2 the boundary-layer flow is calculated numerically and very close to both the leading and trailing edges of the plate the flow is identical to that in the non-rotating case. Goldstein expansions are calculated at both points and the singularity at the trailing edge is examined using triple-deck theory. This demonstrates that for Ro of order E1/2 the E1/4-layer exhibits behaviour similar to that of a classical boundary layer.