Representing the effects of mesoscale eddies in coarse-resolution ocean models

Mesoscale eddies in the ocean mix fluid parcels in a way that is highly constrained by the stratified nature of the fluid—so much so that much of our intuition about ocean mixing comes from thinking in density coordinates. Temporal-residual-mean (TRM) theory provides the link between the different views that are apparent from averaging turbulent flow in height coordinates and in density coordinates. The TRM theory reduces the parameterization problem from three dimensions to two dimensions and it shows how the divergent part of the relevant eddy density flux is skew-symmetric in height coordinates and that the total advection velocity can be adiabatic. The Gent-McWilliams scheme is best interpreted as a scheme for implementing the temporal residual mean. The TRM theory has very specific things to say about how the tracers in coarseresolution models should be interpreted and how the skew diffusion streamfunction should approach zero at boundaries. Here it is emphasized that the extra advection in the TRM theory is not the bolus transport because the extra TRM advection is non-divergent and diapycnal in character while the bolus velocity is divergent and adiabatic. When using eddy-permitting numerical model results to deduce a parameterization for mesoscale eddies, it is very important to use the full TRM theory, and in so doing, the parameterization task is simplified somewhat.