Mixed Layer Mesoscales for OGCMs: Model development and assessment with T/P, WOCE and Drifter data

Abstract

We present a model for mixed layer (ML) mesoscale (M) fluxes of an arbitrary tracer in terms of the resolved fields (mean tracer and mean velocity). The treatment of an arbitrary tracer, rather than only buoyancy, is necessary since OGCMs time step T, S, CO2, etc and not buoyancy. The particular case of buoyancy is used to assess the model results. The paper contains three parts: derivation of the results, discussion of the results and assessment of the latter using, among others, WOCE, T/P and Drifter data. Derivation. To construct the M fluxes, we first solve the ML M dynamic equations for the velocity and tracer M fields. The goal of the derivation is to emphasize the different treatments of the non-linear terms in the adiabatic vs. diabatic ocean (deep ocean vs. mixed layer). Results. We derive analytic expressions for the following variables: a) vertical and horizontal M fluxes of an arbitrary tracer, b) M diffusivity in terms of the EKE, c) surface value of the EKE in terms of the vertical M buoyancy flux together with a model for the z-profile of the M EKE, d) tapering function T(z) in terms of the large scale variables; vanishes at the surface and tends to unity below the ML where the stream function smoothly connects with the deep ocean GM form, e) new eddy induced velocity. Assessment. a) the vertical flux naturally vanishes at the ocean surface, as physically required, b) the second z-derivative of the buoyancy flux is negative, implying re-stratification, in agreement with eddy resolving simulations, c) the predicted surface EKE compares well with the T/P-Jason-1 altimetry data in both intensity and geographical distribution, d) the predicted z-profile of the EKE compares well with WOCE data, e) the model predicts both the z-profile and the surface values of the M diffusivity, f) the latter is in accord with the Global Drifter and T/P data.