On the mixing efficiency in stably stratified turbulence

The mixing efficiency Rf (more formally referred to as the flux Richardson number) is a widely used parameter that is intended to provide a measure of the amount of turbulent kinetic energy (TKE) that is irreversibly converted to background potential energy as a result of turbulent mixing in a stably stratified fluid. In this paper, three different definitions of the mixing efficiency that are commonly used in stratified turbulence are presented to highlight under what flow conditions they might be approximately equivalent and when such equivalences might break down. Analysis of two existing DNS datasets are presented to compare these various definitions. It was found that all three definitions were approximately equal when the gradient Richardson number Rig ≤ 1/4. Conversely, when Rig > 1/4, significant variations are noticeable between the various definitions. Furthermore, the irreversible formulation of Rf is the only definition that is free from oscillations at higher Rig values.