Parameterization of turbulent fluxes and scales using homogeneous sheared stably stratified turbulence simulations

Laboratory experiments on stably stratified grid turbulence have suggested that turbulent lent diffusivity kappa(p) can be expressed in terms of a turbulence activity parameter epsilon/vN(2), with different power-law relations appropriate for different levels of epsilon/vN(2) . To further examine the applicability of these findings to both a wider range of the turbulence intensity parameter epsilon/vN2 and different forcing mechanisms, DNS data of homogeneous sheared stratified turbulence generated by Shih et al. (2000) and Venayagamoorthy et al. (2003) are analysed in this study. Both scalar eddy diffusivity kappa(p) and eddy Viscosity kappa(v) are found to be well-correlated with epsilon/vN(2), and three distinct regimes of behaviour depending on the value of epsilon/vN(2) are apparent. In the diffusive regime D, corresponding to low values of epsilon/vN(2) and decaying turbulence, the total diffusivity reverts to the molecular value; in the intermediate regime I, corresponding to 7 < epsilon IvN(2) < 100 and stationary turbulence, diffusivity exhibits a linear relationship with epsilon/vN(2), as predicted by Osborn (1980); finally, in the energetic regime E, corresponding to higher values of epsilon/vN(2) and growing turbulence, the diffusivity scales with (epsilon/vN(2))(1/2). The dependence of the flux Richardson number R-f on epsilon/vN(2) explains the shift in power law between regimes I and E. Estimates for the overturning length scale and velocity scales are found for the various epsilon/vN(2) regimes. It is noted that epsilon/vN(2) similar to Re/Ri similar to ReFr2, suggesting that such Reynolds-Richardson number or Reynolds-Froude number aggregates are more descriptive of stratified turbulent flow conditions than the conventional reliance on Richardson number alone.