Vorticity balance of boundary currents

Abstract

Friction at the seafloor acts as a source of potential vorticity or in (PV) for individual isopycnic layers of a boundary current. The rate of PV transport (flux times layer thickness) equals, to a good approximation, the divergence of alongstream shear stress in the bottom boundary layer at the seafloor, which in turn equals the alongstream gradient of Montgomery potential. Mean PV transport is continuous along isopycnals between the bottom boundary layer and a boundary current in statistically steady state. Within the boundary current, Reynolds flux of vorticity transports PV. The divergence of this transport balances planetary vorticity advection and other terms in the vorticity equation. PV transport is equivalent to horizontal shear force, and its continuity from the seafloor to the interior of the boundary current implies that the total shear force exerted by the seafloor over the broad footprint of an isopycnic layer acts as much increased shear over the shallow depth of the same layer offshore. A drag law of the bottom boundary layer connects shear stress at the seafloor to velocity outside the boundary layer, a similarity argument yields the functional form of the shear stress gradient-friction velocity relationship, and hence the boundary condition on PV transport from the seafloor. This is neither free-slip nor no-slip, but closer to the latter