A Constraint of Potential Vorticity on the Abyssal Ocean Circulation

This study considers some consequences of potential vorticity (PV) balance in simple source-sink flows calculated with a reduced-gravity model of an abyssal ocean layer. The requirement to dissipate the PV flux associated with the water-mass inflow/outflow largely determines the most intense boundary currents. This PV constraint can be best demonstrated in the linear model by comparing circulation patterns driven by a downwelling source and by an inflow through a side boundary such as occurs in a marginal sea overflow. In either case the abyssal layer receives planetary PV along with the water-mass source. In the open-ocean convection case, the downward vertical velocity squashes vortex lines which produces a compensating negative PV (northern hemisphere). Thus downwelling makes no contribution to the PV budget. A boundary inflow, in contrast, makes a nontrivial contribution to the PV budget that must be balanced (in steady state) with the net PV production due to frictional effects. The different PV balance in the two cases is reflected in quite different circulation patterns, especially in the boundary layers. This PV constraint also controls, to some extents, the water-mass exchanges between two basins.