Mixed layer mesoscales: a parameterization for OGCMs

Abstract. We derive and assess a parameterization of the mixed layer vertical and horizontal mesoscale fluxes of an arbitrary tracer. The results, which are obtained by solving the mesoscale dynamic equations and contain no adjustable parameters, are expressed in terms of the large scale fields resolved by coarse resolution OGCMs (ocean global circulation models).

The new model can be put in the right perspective by considering the following. Thus far, the lack of a mixed layer mesoscale model that naturally satisfies the required boundary condition (the vertical flux must vanish at the surface), was remedied by extending the stream function modeled for the adiabatic deep ocean into the mixed layer using an arbitrary tapering function chosen to enforce the required boundary condition. The present model renders the tapering schemes unnecessary for the vertical flux automatically vanishes at the ocean surface. The expressions we derive for the vertical and horizontal mesoscale fluxes are algebraic and should be used in conjunction with any of the available mesoscale models valid in the adiabatic deep ocean.

We also discuss a new feature representing the effect of sub-mesoscales on mesoscales. It is shown that in the case of strong wind, one must add to the mean Eulerian velocity that enters the parameterization of the mesoscale fluxes a new term due to sub-mesoscales whose explicit form we work out.

The assessment of the model results is as follows. First, previous eddy resolving results indicated a robust re-stratification effect by mesoscales; we show that the model result for the mesoscale vertical flux leads to re-stratification (its second z-derivative is negative) and that it is of the same order of magnitude but opposite sign of the vertical flux by small scale turbulence, leading to a large cancellation. Second, since mesoscales act as a source of the eddy kinetic energy, we compare the predicted surface values vs. the Topex-Poseidon. Third, we carry out an eddy resolving simulation and assess both z-profile and magnitude of the model vertical flux against the simulation data. The tests yield positive results.

A more stratified mixed layer has implication for the oceanic absorption of heat and CO₂, a feature whose implications on climate predictions we hope to explore in the future.