Implications of inertial subrange scaling for stably stratified mixing

The effects of turbulent dynamic range on scalar mixing in stably stratified turbulence are investigated by an adaptation of the theoretical passive scalar modelling arguments of Beguier et al. (1978) and demonstrated statistically using direct numerical simulations of statistically stationary homogeneous stratified and sheared turbulence (SHSST). By analysis of inertial and inertial-convective subrange scaling, we show that the relationship between active scalar and turbulence time scales is predicted by the ratio of the Kolmogorov and Oboukhov-Corrsin constants provided there is sufficient scale separation for inertial and inertial-convective subrange scalings to be valid. With this analysis, we show that the turbulent mixing coefficient, $\Gamma \equiv \chi/\epsilon$, that is, within this context defined to be the ratio of available potential energy ($E_p$) and turbulent kinetic energy ($E_k$) dissipation rates, can be estimated by $E_p,E_k$ and a universal constant provided a Reynolds number is sufficiently high, observed here at $Re_b \equiv \epsilon / \nu N^2 \gtrapprox 300$ where $\nu$ is the kinematic viscosity and $N$ is the characteristic buoyancy frequency. We propose a model for diapycnal mixing with robust theoretical parametrisation and asymptotic behaviour in this high-$Re_b$ limit.