Vorticity balance of boundary currents

Abstract

Friction at thc seafloor acts as a source of potential vorticity (PV) for individual isopycnic layers of a boundary current. The rate of PV transport (flux times !ayer thickness) equals, to a good approximation, the divergence of alongstream shear stress in the bottom boundary !ayer at the seafloor, which in turn equals the alongstream gradient of Montgomery potential. Mean PV transport is continuous along isopycnals between the bottom boundary !ayer 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 othcr tcrms in the vorticity cquation. PV transport is cquivalent to horizontal shcar force, and its continuity from the seatloor to thc interior of thc boundary eurrent implies that the total shear force exerted by thc seafloor over the broad footprint of an isopycnic !ayer acts as much increased shear over the shallow dcpth of the same !ayer o/fahorc. A drag law of the bottom boundary !ayer connects shear stress at the seafloor to velocity outside the boundary !ayer, 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.