Nonlinear stratified spindown over a sloping bottom

The nonlinear modification of stratified spindown is analytically and numerically examined for an initially barotropic flow with lateral shear over a sloping bottom. Ekman advection of buoyancy creates buoyancy anomalies that reduce the Ekman transport by thermal wind shear and hence suppress spindown by weakening Ekman pumping and suction. For increasing Rossby number, Ekman pumping is weakened to a greater extent than Ekman suction. The analytical theory shows that this asymmetry is primarily a result of nonlinear advection of buoyancy rather than momentum, in contrast to previous theoretical calculations for the spindown of a barotropic flow over a flat bottom in an unstratified fluid. The results of this study are applied to currents on the continental slope.