Some insights to infer turbulent diapycnal mixing in geophysical flows

In this study, some new insights for inferring diapycnal diffusivity K_ρ in stably stratified flows are provided based on physical scaling arguments and tested using high resolution direct numerical simulation (DNS) data. It is shown that for weakly stratified flows where buoyancy effects are not dominant, the eddy diffusivity K_ρ∼ w' L_E. Here L_E is the Ellison length scale that represents the outer scale of turbulence and w' is the vertical turbulent velocity scale. For the strongly stratified regime, this scaling overpredicts the true diapycnal diffusivity due to internal wave induced adiabatic motions. In order to infer K_ρ in the limit of strong stratification, a new formulation for K_ρ is provided using w', L_E and turbulent Froude number Fr=ε/Nk, wherein N is the buoyancy frequency, k is the turbulent kinetic energy and ε is the rate of dissipation of turbulent kinetic energy, respectively. The comparison between the proposed formulation and exact diffusivities using DNS data is remarkable and highlights the strength of the proposed new parameterization in its ability to predict turbulent mixing in stably stratified geophysical flows.