The Barotropic Rossby Wave Drag Due to an Isolated Topography

Abstract

A formula for the barotropic Rossby wave drag exerted by an arbitrary shallow topography on a homogeneous eastward flow is obtained under the requirements that U/f0L?1, hM/H=O(U/f0L) and L<LW≡(U/?)½, where U is the speed of the flow, hM, the maximum height of the topography, L the horizontal scale of the topography and H the vertical distance between the horizontal planes confining the flow. The drag force,where V is the volume of the topography, Γ(≡f0V/H) is the topographically induced circulation, and Xk?,Yk?=??(Xk,Yk)h(x,y)dxdy/V. A typical case is computed and the wave drag per unit area is found to be approximately 1.3 N m?2. This implies an energy dissipation rate of 20 W m?2 which is comparable to the kinetic energy generated in a cyclone, and is several times that due to frictional dissipation. The effects of stratification and compressibility are discussed; the former generally has no effect on the drag while the latter increases the drag by a factor of 1.6.