Direct numerical simulations are performed to compare the evolution of turbulent stratified shear layers with different density gradient profiles at a high Reynolds number. The density profiles include uniform stratification, two-layer hyperbolic tangent profile and a composite of these two profiles. All profiles have the same initial bulk Richardson number (\(Ri_{b,0}\)); however, the minimum gradient Richardson number and the distribution of density gradient across the shear layer are varied among the cases. The objective of the study is to provide a comparative analysis of the evolution of the shear layers in term of shear layer growth, turbulent kinetic energy as well as the mixing efficiency and its parameterization. The evolution of the shear layers in all cases shows the development of Kelvin–Helmholtz billows, the transition to turbulence by secondary instabilities followed by the decay of turbulence. Comparison among the cases reveals that the amount of turbulent mixing varies with the density gradient distribution inside the shear layer. The minimum gradient Richardson number and the initial bulk Richardson number do not correlate well with the integrated TKE production, dissipation and buoyancy flux. The bulk mixing efficiency for fixed \(Ri_{b,0}\) is found to be highest in the case with two-layer density profile and lowest in the case with uniform stratification. However, the parameterizations of the flux coefficient based on buoyancy Reynolds number and the ratio of Ozmidov and Ellison scales show similar scaling in all cases.

进行直接数值模拟以比较在高雷诺数下具有不同密度梯度剖面的湍流分层剪切层的演变。密度剖面包括均匀分层、两层双曲正切剖面和这两种剖面的复合。所有配置文件都具有相同的初始批量理查森数 ( \(Ri_{b,0}\)); 然而，最小梯度理查森数和跨剪切层的密度梯度分布在不同情况下是不同的。该研究的目的是对剪切层的演变在剪切层生长、湍流动能以及混合效率及其参数化方面进行比较分析。在所有情况下，剪切层的演变都显示了开尔文-亥姆霍兹波的发展，通过二次不稳定性过渡到湍流，然后是湍流的衰减。案例之间的比较表明，湍流混合量随剪切层内的密度梯度分布而变化。最小梯度理查森数和初始体积理查森数与综合 TKE 生产、耗散和浮力通量的相关性不高。\(Ri_{b,0}\)在两层密度分布的情况下最高，在均匀分层的情况下最低。然而，基于浮力雷诺数和 Ozmidov 和 Ellison 比例的通量系数参数化在所有情况下都显示出相似的比例。