Slope control in Western boundary currents

Abstract

An analytic solution is presented for the steady-state depth-averaged western boundary current flowing over the continental slope by combining three highly idealized models: the Stommel model, the Munk model, and the arrested topographic wave model. The main vorticity balance over the slope is between planetary vorticity advection and the slope-induced bottom stress torque, which is proportional to rv(h-1)x where r is the Rayleigh friction coefficient, h is the water depth, and v is the meridional velocity. This slope-induced torque provides the necessary source of vorticity for poleward flow over the slope, its simple interpretation being that vorticity is produced because the bottom stress has to act over the seaward-deepening water column. The character of the solution depends on the slope α as well as on the assumed bottom drag coefficient, and the length scale of the boundary current is ∼√2r/(βα). It is further shown that, if the depth-averaged velocity flows along isobaths, then the stretching of water columns associated with cross-isobath geostrophic flow, which compensates bottom Ekman transport, is identical to the slope-induced torque by the geostrophic velocities.