Effect of rotation on mixing efficiency in homogeneous stratified turbulence using unforced direct numerical simulations

Abstract

Diapycnal (irreversible) mixing is analyzed using thirty direct numerical simulations (at \(1024^3\) resolution) of homogeneous rotating stratified turbulence (RST) in the absence of imposed shear or forcing. The influence of varied rotation and stratification rates on the energetics (in particular the dissipation rates of kinetic and potential energies) is presented. Data is also analyzed within a new parametric framework, using the turbulent Froude and Rossby numbers \(Fr_t = \epsilon /Nk\), \(Ro_t = \epsilon / f k\), where k is the turbulent kinetic energy, \(\epsilon\) its rate of dissipation, N the buoyancy frequency and f the Coriolis parameter. This framework is used to illustrate relative magnitudes of the stratification and rotation in geophysical flows and provide a useful tool for explicating the relationship between \(Fr_t\) and \(Ro_t\) as relevant dynamic parameters in the geophysical setting. Results indicate that unforced rotation does not impact the magnitude of the irreversible mixing coefficient (\(\Gamma =\epsilon _P/\epsilon\)) when compared to results without rotation, where \(\epsilon _P\) is the rate of potential energy dissipation. Moreover, it is shown that the recent scaling laws for mixing efficiency in stably stratified turbulence in the absence of rotation, as exemplified in Garanaik & Venayagamoorthy (J. Fluid Mech. 867, 2019, pp. 323-333), are applicable as well for homogeneous and decaying RST. Results also highlight the ambiguity of the ratio N/f as a control parameter for the classification of small-scale RST, and thus for evaluating diapycnal mixing.