Mixing efficiency in stratified turbulence

We consider mixing of the density field in stratified turbulence and argue that, at sufficiently high Reynolds numbers, stationary turbulence will have a mixing efficiency and closely related mixing coefficient described solely by the turbulent Froude number Fr = epsilon(k)/(Nu(2)), where epsilon(k) is the kinetic energy dissipation, u is a turbulent horizontal velocity scale and N is the Brunt-Vaisala frequency. For Fr >> 1, in the limit of weakly stratified turbulence, we show through a simple scaling analysis that the mixing coefficient scales as Gamma proportional to Fr-2, where Gamma = epsilon(p)/epsilon(k) and epsilon(p) is the potential energy dissipation. In the opposite limit of strongly stratified turbulence with Fr << 1, we argue that should reach a constant value of order unity. We carry out direct numerical simulations of forced stratified turbulence across a range of Fr and confirm that at high Fr, Gamma proportional to Fr-2, while at low Fr it approaches a constant value close to Gamma = 0:33. The parametrization of based on Re-b due to Shih et al. (J. Fluid Mech., vol. 525, 2005, pp. 193-214) can be reinterpreted in this light because the observed variation of Gamma in their study as well as in datasets from recent oceanic and atmospheric measurements occurs at a Froude number of order unity, close to the transition value Fr = 0.3 found in our simulations.