Environmental Fluid Dynamics Laboratories, Department of Civil Engineering and Geological Sciences, University of Notre Dame, Notre Dame, IN 46556, USA.
Philos Trans A Math Phys Eng Sci. 2013 Jan 13;371(1982):20120213. doi: 10.1098/rsta.2012.0213.
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.
有人认为，自然发生的分层剪切流的混合效率，γ=Rf/(1-Rf)，其中 Rf 是通量理查森数，取决于至少两个控制参数：梯度理查森数 Ri 和浮力雷诺数 Re(b)=ε/vN(2)。研究发现，在大约 0.03<Ri<0.4 的范围内，跨越 10(4)<Re(b)<10(6)，通过直接测量稳定大气边界层中的通量和属性梯度以及湍流动能耗散（TKE）的均匀/稳定平衡方程获得的混合效率与使用标量平衡方程评估的混合效率大致相似。在这些 Ri 和 Re(b)范围之外，基于 TKE 方程均匀性和稳定性的常用通量估计方法失效（例如浮力效应不重要，能量通量散度显著或流动非稳态）。在较宽的范围内，0.002<Ri<1，混合效率随 Ri 增加而增加，但随 Re(b)增加而减小。当 Ri 接近 Ri(cr)∼0.1-0.25 时，可以认为 γ 是一个常数γ≈0.16-0.2。这些结果揭示了先前研究中注意到的γ的广泛可变性。
