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 Γ α ( α stands for heat, salt and momentum). However, to compute the diffusivities, one needs additional information, specifically, the dissipation ε. 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 Γ α ’s are functions of both Ri and R ρ (Richardson number and density ratio representing double diffusion, DD); the Γ α are different for heat, salt and momentum; in the case of heat, the traditional value Γ h = 0.2 is valid only in the presence of strong shear (when DD is inoperative) while when shear subsides, NATRE data show that Γ h can be three times as large, a result that we reproduce. The salt Γ s is given in terms of Γ h . The momentum Γ m has thus far been guessed with different prescriptions while the RSM provides a well defined expression for Γ m ( Ri, R ρ ). Having tested Γ h , we then test the momentum Γ m by showing that the turbulent Prandtl number Γ m / Γ h vs. Ri reproduces the available data quite well. As for the dissipation ε, 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 εN −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 Γ α = 0.2 with the RSM result that brings into the problem the Ri, R ρ dependence of the Γ α ; 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 dat