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 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.