Stratified Flow along a Corrugated Slope: Separation Drag and Wave Drag

Abstract

Lee wave generation and horizontal flow separation in stratified flow along a slope, with corrugations or a ridge running directly downslope, are explored using analytical and numerical methods. Both of these processes are important to the drag on alongslope currents. The analytical solution for steady wave generation by stratified flow along a corrugated slope is extended to the evanescent flow regimes. There are two evanescent regimes, having intrinsic frequencies either above the buoyancy frequency N (fast flow), or below N sin(a) (slow flow), for nonrotating fluid and slope angle, a. Streamlines of the low speed evanescent solution tend to follow isobaths, while those of wave solutions tend to flow up over ridges and down in canyons. An analytical expression is developed for the wave drag felt by an isolated ridge on a slope. For a Gaussian ridge of alongslope length L, the drag becomes small when U/LN > 1 (the fast flow regime), or when U/(LN sin a) < 1/2 (the slow flow regime). Numerical experiments are performed for stratified flow along a slope with an isolated ridge. The ridge height is varied and the pressure drag on the ridge evaluated for flow in the wave-generating and slow evanescent regimes. The slow-flow case gives rise to a large region of horizontal (isopycnal) flow separation with proportionally stronger relative vorticity in the wake than the wave-generating case. Pressure drag coefficients based on projected frontal area are similar for both cases, increase linearly with the corrugation amplitude, and level off around a value of 1?1.2.