Derivation and assessment of a mixed layer sub-mesoscale model

Abstract

Abstract. Present studies of mixed layer sub-mesoscales rely primarily on high resolution numerical simulations. Only few of these studies have attempted to parameterize the ensuing buoyancy submesoscale fluxes in terms of the resolved fields so that they can be used in OGCMs (ocean circulation models) that do not resolve sub-mesoscales. In reality, OGCMs used in climate studies include a carbon-cycle which also requires the flux of a passive tracer. The goal of this work is to derive and assess a parameterization of the submesoscale vertical flux of an arbitrary tracer in terms of the resolved fields. The parameterization is obtained by first solving the dynamic equations governing the velocity and tracer fields that describe sub-mesoscales and then constructing second-order moments such as the tracer fluxes. A key ingredient of the present approach is the modeling of the non-linear terms that enter the dynamic equations of the velocity and tracer fields, a problem that we discuss in two Appendices. The derivation of the sub-mesoscale tracer vertical flux is analytical and can be followed in detail since no additional information is required. The external forcing includes both baroclinic instabilities and wind stresses. We compare the model results with data from sub-mesoscale resolving simulations available in the literature which are of two kinds, one with no wind (baroclinic instabilities only) and the other with both baroclinic instabilities and wind. In both cases, the model results reproduce the simulation data satisfactorily.