Models of ocean circulation based on the residual circulation

We formulate a model of ocean circulation in which the prognostic variable is the ``residual circulation.'' The effect of eddies appears as an eddy potential vorticity (PV) flux force in the momentum equations. We argue that the residual circulation (i) is the natural framework in which to develop coarse resolution ocean models (ii) leads to important conceptual insights in to the nature of eddy-mean-flow interaction (iii) suggests refinements to the parameterization of eddies in ocean models (e.g the role of the beta effect and the nature of the upper boundary condition involving the interaction of eddies with the mixed layer) and (iv) is readily implemented in ocean climate models.

If we assume the divergent part of the eddy PV flux on isopycnal surfaces is directed down the mean PV gradient, the resulting expression for the flux in height coordinate is made of a relative vorticity, beta, and stretching contributions. We implement and test our scheme in a coarse resolution configuration of the MIT ocean circulation model using an idealized sector-channel geometry with a flat bottom and one active tracer. The model is forced both mechanically and thermodynamically. We conduct a series of experiments in which the sensitivity of the solution to the formulation of the PV flux ``force'' is studied. We also experiment with different choices of boundary conditions for the PV flux. Finally, the scheme is implemented in a global version of the MIT model (at a horizontal resolution of 2.8 degrees) forced by realistic wind-stress and heat and freshwater fluxes.