Slope control in western boundary currents

An analytic solution is presented for the steady-state depth-averaged weste rn boundary current flowing over the continental slope by combining three h ighly idealized models: the Stommel model, the Munk model, and the arrested topographic wave model. The main vorticity balance over the slope is betwe en planetary vorticity advection and the slope-induced bottom stress torque , which is proportional to rv(h(-1))(x) where r is the Rayleigh friction co efficient, h is the water depth, and v is the meridional velocity. This slo pe-induced torque provides the necessary source of vorticity for poleward f low over the slope, its simple interpretation being that vorticity is produ ced because the bottom stress has to act over the seaward-deepening water c olumn. The character of the solution depends on the slope alpha as well as on the assumed bottom drag coefficient, and the length scale of the boundar y current is similar to root 2r(beta alpha). It is further shown that, if t he depth-averaged velocity flows along isobaths, then the stretching of wat er columns associated with cross- isobath geostrophic flow, which compensat es bottom Ekman transport, is identical to the slope-induced torque by the geostrophic velocities.