Turbulent Diffusivities for Momentum, Heat, Salt and Passive Scalars
A program began ten years ago to build a turbulence model to describe high Reynolds numbers flows. Specifically, the aim was to devise a model that would satisfy two basic conditions: reproduce available turbulence data (laboratory, numerical simulations, etc.) concerning shear driven flows, buoyancy driven flows, 2D turbulence, freely decaying turbulence etc., and yet be manageable so as to be used, for example, in General Circulation Models (GCM'S). The model was presented in a series of papers that have appeared in Physics of Fluids since 1996. A total of about 80 turbulence statistics were reproduced. The model has no adjustable parameters. The next step was to apply the model to construct the vertical diffusities K for moment K(sub m), temperature K(sub h), salt K(sub s). and passive scalars K(sub c). First, we took K(sub s) = K(sub h) and tested the model using the GFDL ocean model. The results for the profiles of T and S vs. depth are indistinguishable from those derived using the latest model, the KPP model by the NCAR group. Presently, we are running the same Geophysical Fluid Dynamics Laboratory (GFDL) code relaxing the assumptive K(sub s) = K(sub h). Indeed, the turbulence model yields a salt diffusivity that depends on Ri and R rho (= Beta delta S/delta z/alpha delta T/delta z) in such a way that K(sub s) may be quite different from K(sub h). Salt fingers and double diffusivity laboratory data are reproduced. Results from the ocean model will be available shortly. Finally, we are trying to derive the horizontal diffusivities with the goal of providing a physically acceptable representation of mesoscale eddies. The recently suggested GMW parameterization has improved several O-GCM results and the goal here is to try to derive/justify it from a turbulence model and/or propose improvements/modifications. Theoretical work is in progress.