Mixing efficiency in natural Flows

Abstract

It is argued that the mixing efficiency of naturally occurring stratified shear flows, γ = Rf/(1 - Rf), where Rf is the flux Richardson number, is dependent on at least two governing parameters: the gradient Richardson number Ri and the buoyancy Reynolds number Reb = ε/υN2. It is found that, in the range approximately 0.03 < Ri < 0.4, which spans 104 < Reb < 106, the mixing efficiency obtained via direct measurements of fluxes and property gradients in the stable atmospheric boundary layer and homogeneous/stationary balance equations of turbulent kinetic energy (TKE) is nominally similar to that evaluated using the scalar balance equations. Outside these Ri and Reb ranges, the commonly used flux-estimation methodology based on homogeneity and stationarity of TKE equations breaks down (e.g. buoyancy effects are unimportant, energy flux divergence is significant or flow is non-stationary). In a wide range, 0.002 < Ri < 1, the mixing efficiency increases with Ri, but decreases with Reb. When Ri is in the proximity of Ricr ∼ 0.1-0.25, γ can be considered a constant γ ≈ 0.16-0.2. The results shed light on the wide variability of γ noted in previous studies. © 2012 The Author(s) Published by the Royal Society.