Bryan, K., 1987: Potential vorticity in models of the ocean circulation. Quarterly Journal of the Royal Meteorological Society, 113, 713-734.

Summary: Existing observations suffice to give a qualitative description of the wind-driven and thermohaline components of the ocean circulation, but a hierarchy of analytical and numerical models is now needed for use in coupled occean-atmosphere models of the earth's climate. Potential vorticity is a more appropriate diagnostic field variable than angular momentum for the ocean circulation because of the complicated geometry of ocean basins. Patterns of potential vorticity on surfaces of constant density help validate ocean circulation models, and give physical insight into how the ocean circulation works.

High resolution models suggest that the lateral mixing of potential vorticity by mesoscale eddies along isopycnal surfaces is of the same order as large-scale advection, and that the assumption of inviscid, potential-vorticity-conserving flow in the thermocline is not appropriate for the real ocean. A satisfactory test of this vorticity-conserving flow in the thermocline is not appropriate for the real ocean. A satisfactory test of this conjecture will require the extensive measurements planned for the World Ocean Circulation Experiment.

Models also indicate that the transport of water mass properties by mesoscale eddies is largely a mixing along isopycnal surfaces. The weak temperature gradients along isopycnal surfaces in most areas of the ocean limit the effectiveness of the mesoscale eddies in transporting significant amounts of heat across latitude circles.