Dynamic model of mesoscale eddies. Eddy parameterization for coarse resolution ocean circulation models

In the framework of the eddy dynamic model developed in two previous papers (Dubovikov, M.S., Dynamical model of mesoscale eddies, Geophys. Astophys. Fluid Dyn., 2003, 97, 311-358; Canuto, V.M. and Dubovikov, M.S., Modeling mesoscale eddies, Ocean Modelling, 2004, 8, 1-30 reterred as I-II), we compute the contribution of unresolved mesoscale eddies to the large-scale dynamic equations of the ocean. In isopycnal coordinates, in addition to the bolus velocity discussed in I-II, the mesoscale contribution to the large scale momentum equation is derived. Its form is quite different from the traditional down-gradient parameterization. The model solutions in isopycnal coordinates are transformed to level coordinates to parameterize the eddy contributions to the corresponding large scale density and momentum equations. In the former, the contributions due to the eddy induced velocity and to the residual density flux across mean isopycnals (so called Sigma-term) are derived, both contributions being shown to be of the same order. As for the large scale momentum equation, as well as in isopycnal coordinates, the eddy contribution has a form which is quite different from the down-gradient expression.