Scaling arguments are presented to quantify the widely used diapycnal (irreversible) mixing coefficient $\unicode[STIX]{x1D6E4}=\unicode[STIX]{x1D716}_{PE}/\unicode[STIX]{x1D716}$ in stratified flows as a function of the turbulent Froude number $Fr=\unicode[STIX]{x1D716}/Nk$. Here, $N$ is the buoyancy frequency, $k$ is the turbulent kinetic energy, $\unicode[STIX]{x1D716}$ is the rate of dissipation of turbulent kinetic energy and $\unicode[STIX]{x1D716}_{PE}$ is the rate of dissipation of turbulent potential energy. We show that for $Fr\gg 1$, $\unicode[STIX]{x1D6E4}\propto Fr^{-2}$, for $Fr\sim \mathit{O}(1)$, $\unicode[STIX]{x1D6E4}\propto Fr^{-1}$ and for $Fr\ll 1$, $\unicode[STIX]{x1D6E4}\propto Fr^{0}$. These scaling results are tested using high-resolution direct numerical simulation (DNS) data from three different studies and are found to hold reasonably well across a wide range of $Fr$ that encompasses weakly stratified to strongly stratified flow conditions. Given that the $Fr$ cannot be readily computed from direct field measurements, we propose a practical approach that can be used to infer the $Fr$ from readily measurable quantities in the field. Scaling analyses show that $Fr\propto (L_{T}/L_{O})^{-2}$ for $L_{T}/L_{O}>O(1)$, $Fr\propto (L_{T}/L_{O})^{-1}$ for $L_{T}/L_{O}\sim O(1)$, and $Fr\propto (L_{T}/L_{O})^{-2/3}$ for $L_{T}/L_{O}<O(1)$, where $L_{T}$ is the Thorpe length scale and $L_{O}$ is the Ozmidov length scale. These formulations are also tested with DNS data to highlight their validity. These novel findings could prove to be a significant breakthrough not only in providing a unifying (and practically useful) parameterization for the mixing efficiency in stably stratified turbulence but also for inferring the dynamic state of turbulence in geophysical flows.

structure that is, in places, characterized by strong salinity stratification and multiple inversions in temperature. Here, two short time series from continuously profiling floats, equipped with microstructure sensors to measure subsurface mixing, are used to highlight implications of complex hydrography on upper-ocean heat content and the evolution of sea surface temperature. Weak mixing coupled with the existence of subsurface warm layers suggest the potential for storage of heat below the surface mixed layer over relatively long time scales. On the diurnal time scale, these data demonstrate the competing effects of surface heat flux and subsurface mixing in the presence of thin salinity-stratified mixed layers with temperature inversions. Pre-existing stratification can amplify the sea surface temperature response through control on the vertical extent of heating and cooling by surface fluxes. In contrast, subsurface mixing entrains relatively cool water during the day and relatively warm water during the night, damping the response to daytime heating and nighttime cooling at the surface. These observations hint at the challenges involved in improving monsoon prediction at longer, intraseasonal time scales as models may need to resolve upper-ocean variability over short time and fine vertical scales.

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New insights for inferring diapycnal diffusivity in stably stratified turbulent flows are obtained based on physical scaling arguments and tested using high-resolution direct numerical simulation (DNS) data. It is shown that the irreversible diapycnal diffusivity can be decomposed into a diapycnal length scale that represents an inner scale of turbulence and a diapycnal velocity scale. Furthermore, it is shown that the diapycnal length scale and velocity scale can be related to the measurable Ellison length scale ($L_E$) that represents outer scale of turbulence and vertical turbulent velocity scale ($w^\prime$) through a turbulent Froude number scaling analysis. The turbulent Froude number is defined as $Fr=\epsilon/Nk$, where $\epsilon$ is the rate of dissipation of turbulent kinetic energy, $N$ is the buoyancy frequency, and $k$ is the turbulent kinetic energy. The scaling analysis suggests that the diapycnal diffusivity $K_\rho \sim w^\prime L_E$ in the weakly stratified regime ($Fr&gt;1$) and $K_\rho \sim (w^\prime L_E )\times Fr $ for the strongly stratified regime ($Fr&lt;1$).

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