Rotating flow over a step

Abstract

The flow of a rotating homogeneous incompressible fluid over a step is investigated. In the physical system considered the rotation axis is vertical and the step, which is assumed to be infinitely long, is located on a horizontal plane surface. Upstream of the step the fluid is in a uniform free stream motion at an angle α to a line perpendicular to the step axis. The analysis is restricted by the following: E [Lt ] 1, Ro ∼ E^½, h/D ∼ E^½, H/D ∼ E⁰, and cos α ∼ E⁰ where Ro and E are the Rossby and Ekman numbers and h/D and H/D are the step height to step width and water depth to step width ratios respectively. The flow field is shown to consist of interior geostrophic regions, Ekman layers on the horizontal surfaces and vertical shear layers located in the vicinity of vertical planes defined by the edges of the step. In the vertical layers there is a balance between the inertial, Coriolis, and pressure terms in the momentum equations while the effects of viscosity are found to be negligible. Downstream of the step the streamlines are shifted to the right (positive or Northern Hemisphere rotation) of their upstream locations by a distance of S = 2^½(h/D) E^−½ cos α. Experiments are presented which are in good agreement with the theory advanced.