Ocean turbulence, III: New GISS vertical mixing scheme

We have found a new way to express the solutions of the RSM (Reynolds Stress Model) equations that allows us to present the turbulent diffusivities for heat, salt and momentum in a way that is considerably simpler and thus easier to implement than in previous work. The RSM provides the dimensionless mixing efficiencies Gamma(alpha) (alpha stands for heat, salt and momentum). However, to compute the diffusivities, one needs additional information, specifically, the dissipation epsilon. Since a dynamic equation for the latter that includes the physical processes relevant to the ocean is still not available, one must resort to different sources of information outside the RSM to obtain a complete Mixing Scheme usable in OGCMs. As for the RSM results, we show that the Gamma(alpha)'s are functions of both Ri and R-rho (Richardson number and density ratio representing double diffusion, DD); the Gamma(alpha) are different for heat, salt and momentum; in the case of heat, the traditional value Gamma(h) = 0.2 is valid only in the presence of strong shear (when DD is inoperative) while when shear subsides, NATRE data show that rh can be three times as large, a result that we reproduce. The salt Gamma(s) is given in terms of Gamma(h). The momentum Gamma(m) has thus far been guessed with different prescriptions while the RSM provides a well defined expression for Gamma(m)(Ri,R-rho). Having tested Gamma(h), we then test the momentum Gamma(m) by showing that the turbulent Prandtl number Gamma(m)/Gamma(h) vs. Ri reproduces the available data quite well. As for the dissipation epsilon, we use different representations, one for the mixed layer (ML), one for the thermocline and one for the ocean's bottom. For the ML, we adopt a procedure analogous to the one successfully used in PB (planetary boundary layer) studies; for the thermocline, we employ an expression for the variable epsilon N-2 from studies of the internal gravity waves spectra which includes a latitude dependence; for the ocean bottom, we adopt the enhanced bottom diffusivity expression used by previous authors but with a state of the art internal tidal energy formulation and replace the fixed Gamma(alpha) = 0.2 with the RSM result that brings into the problem the Ri, R-rho dependence of the Gamma(alpha); the unresolved bottom drag, which has thus far been either ignored or modeled with heuristic relations, is modeled using a formalism we previously developed and tested in PBL studies. We carried out several tests without an OGCM. Prandtl and flux Richardson numbers vs. Ri. The RSM model reproduces both types of data satisfactorily. DD and Mixing efficiency Gamma(h)(Ri,R-rho). The RSM model reproduces well the NATRE data. Bimodal epsilon-distribution. NATRE data show that epsilon(Ri < 1) approximate to 10 epsilon(Ri > 1), which our model reproduces. Heat to salt flux ratio. In the Ri >> 1 regime, the RSM predictions reproduce the data satisfactorily. NATRE mass diffusivity. The z-profile of the mass diffusivity reproduces well the measurements at NATRE. The local form of the mixing scheme is algebraic with one cubic equation to solve. Published by Elsevier Ltd.