Laboratory experiments on stably stratified grid turbulence have suggested that turbulent diffusivity $\kappa_\rho$ can be expressed in terms of a turbulence activity parameter $\epsilon/\nu N^2$, with different power-law relations appropriate for different levels of $\epsilon/\nu N^2$. To further examine the applicability of these findings to both a wider range of the turbulence intensity parameter $\epsilon/\nu N^2$ 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 $\kappa_\rho$ and eddy viscosity $\kappa_\nu$ are found to be well-correlated with $\epsilon/\nu N^2$, and three distinct regimes of behaviour depending on the value of $\epsilon/\nu N^2$ are apparent. In the diffusive regime $D$, corresponding to low values of $\epsilon/\nu N^2$ and decaying turbulence, the total diffusivity reverts to the molecular value; in the intermediate regime $I$, corresponding to $7 \,{<} \epsilon/\nu N^2 \,{<}\, 100$ and stationary turbulence, diffusivity exhibits a linear relationship with $\epsilon/\nu N^2$, as predicted by Osborn (1980); finally, in the energetic regime $E$, corresponding to higher values of $\epsilon/\nu N^2$ and growing turbulence, the diffusivity scales with $(\epsilon/\nu N^2)^{1/2}$. The dependence of the flux Richardson number $R_f$ on $\thing$ 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 $\epsilon/\nu N^2$ regimes. It is noted that $\epsilon/\nu N^2 \,{\sim}\, \hbox{\it Re}/\hbox{\it Ri}\,{\sim}\,\hbox{\it ReFr}^2$, 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.

Homogeneous sheared stratified turbulence was simulated using a DNS code. The initial turbulent Reynolds numbers (Re) were 22, 44, and 89, and the initial dimensionless shear rate (S*) varied from 2 to 16. We found (similarly to Rogers (1986) for unstratified flows) the final value of S* at high Re to be ∼ 11, independent of initial S*. The final S* varies at low Re, in agreement with Jacobitz et al. (1997). At low Re, the stationary Richardson number (Ris) depends on both Re and S*, but at higher Re, it varies only with Re. A scaling based on the turbulent kinetic energy equation which suggests this result employs instantaneous rather than initial values of flow parameters.At high Re the dissipation increases with applied shear, allowing a constant final S*. The increased dissipation occurs primarily at high wavenumbers due to the stretching of eddies by stronger shear. For the high-Re stationary flows, the turbulent Froude number (Frt) is a constant independent of S*. An Frt-based scaling predicts the final value of S* well over a range of Re. Therefore Frt is a more appropriate parameter for describing the state of developed stratified turbulence than the gradient Richardson number.

We conduct a parametric study of diapycnal mixing using one-dimensional-turbulence (ODT) simulations. Homogeneous sheared stratified turbulence is considered. ODT simulations reproduce the intermediate and energetic regimes of mixing, in agreement with previous work, but do not capture important physics of the diffusive regime. ODT indicates Kρ~ɛ/N2 for the intermediate regime, and Kρ~(ɛh4)1/3 for the energetic regime and limit of near-zero stratification. Here Kρ is the turbulent diffusivity for mass, ɛ the dissipation rate, N the buoyancy frequency, and h the computational domain height, where h is relevant mainly in simulations with jump-periodic vertical boundary conditions. These scaling relationships suggest that Kρ is independent of the molecular diffusivity. ODT results for a wide range of parameters show that Kρ cannot be parametrized solely with the turbulent intensity parameter ɛ/(νN2), in contrast with the previous studies, but it is well predicted by correlations using the Ellison length scale.

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