A comparative study of turbulent stratified shear layers: effect of density gradient distribution

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.