The quest for an unambiguous parameterization of mixing efficiency in stably stratified geophysical flows

Estimates of turbulent mixing in geophysical settings typically depend on the efficiency at which shear-driven turbulence mixes density across isopycnals. To date, however, no unifying parameterization of diapycnal mixing efficiency exists due to the variability of natural flows and also due to certain ambiguities that arise from descriptions based on a single parameter. Here we highlight important ambiguities of some common single-parameter schemes in the context of a multiparameter framework that considers the independent effects of shear, buoyancy, and viscosity. Parameterizations based on the gradient Richardson number (Ri), the turbulent Froude number (Fr-T), and the buoyancy Reynolds number (Re-b) are considered. The diagnostic ability of these parameters is examined using published data from both direct numerical simulations and field observations.