The forces due to geostrophic flow over shallow topography

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Abstract
The flow of barotropic fluid over an isolated hill in a rapidly rotating system is examined by the numerical solution of the barotropic vorticity equation in which the effects of Ekman boundary layers have been retained. The force due to pressure variations across the hill, which can be decomposed into components at right angles to the incident flow (the “lift” force) and parallel to the incident flow (the “drag” force), is typically of the order 2ρΩUV (ρ being the density of the fluid, Ω the angular velocity of the system, U the incident flow velocity and V the volume of the hill). In the steady state, the drag force is generally small compared to the lift force, but in the early transient stages of the evolution of the flow, the drag force may be as large as 2ρΩUV. It is shown that when the hill is sufficiently high and the Ekman number sufficiently small, nonlinear effects in the vicinity of the hill can greatly prolong this period of transient behaviour. This effect may be important in a number of geophysical contexts where a fluctuating flow impinges on topography.

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