Modeling mesoscale eddies

The mesoscale flux that enters the momentum equations is also contributed by two types of terms of the same physical nature as those entering the thickness flux. The potential vorticity flux is also shown to contain two types of terms: the first is of the gradient-type while the other terms entail the velocity of the mean flow. An expression is derived for the mesoscale diffusivity κM and for the mesoscale kinetic energy K in terms of the large-scale fields. The predicted κM(z) agrees with that of heuristic models. The complete mesoscale model in isopycnal coordinates is presented in Appendix D and can be used in coarse resolution ocean global circulation models.