Mixing efficiency in natural flows

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 Re(b)=ε/vN(2). It is found that, in the range approximately 0.03<Ri<0.4, which spans 10(4)<Re(b)<10(6), 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 Re(b) 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 Re(b). When Ri is in the proximity of Ri(cr)∼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.