Irreversible mixing in stably-stratified turbulence under momentum and scalar forcing: beyond the turbulent Froude number

Mixing coefficient (Γ) parameterizations play a key role in estimating vertical diffusivities of buoyancy (e.g., Osborn model, 1980) in general circulation models. Because of this, there has been continued interest in finding universal descriptions of Γ for stratified turbulent flows. Notably, Γ has been long studied as a function of the buoyancy Reynolds number and, more recently, as a function of the turbulent Froude number with varying degrees of success. In this study, we conducted direct numerical simulations (DNS) of stably-stratified turbulence with both momentum and scalar forcing. Momentum and scalar forcing were linear in the velocity and scalar fields, respectively. In the absence of scalar forcing, Γ from our DNS generally agrees with the turbulent Froude number scalings from Garanaik and Venayagamoorthy (2019). When scalar forcing is present, however, Γ exhibits large variations at fixed values of the turbulent Froude number, indicating that additional parameters need to be considered. We study the turbulence energetics as a function of the relative strengths of momentum and scalar forcing to the background stratification and explore other candidate parameters for collapsing Γ. We also show that Γ can be kept constant by temporally varying the momentum and scalar forcing. Taken together, these results emphasize that the mixing efficiency is strongly influenced by the specific details of the turbulence generation mechanism.