Flow of grounded abyssal ocean currents along zonally-varying topography on a rotating sphere

A steady nonlinear planetary–geostrophic model in spherical coordinates is presented describing the hemispheric-scale meridional flow of grounded abyssal currents on a zonally-sloping bottom. The model, which corresponds mathematically to a quasi-linear hyperbolic partial differential equation, can be solved explicitly for a cross-slope isopycnal field that is grounded (i.e. intersects the bottom on the up slope and down slope sides). As a consequence of the conservation of potential vorticity, the abyssal currents possess decreasing thickness in the equatorward direction while maintaining constant meridional volume transport. There is a small westward zonal transport in the interior of these currents that results in westward intensification as they flow toward the equator. Conditions for the possible formation of a shock to develop on the up slope flank of the current are derived.