Evolution of an initially turbulent stratified shear layer

Direct numerical simulations of a stratified shear layer are performed for several different values of Reynolds, bulk Richardson, and Prandtl numbers. Unlike previous numerical studies, the initial perturbations are turbulent. These initial broadband perturbations do not allow the formation of distinct coherent structures such as Kelvin-Helmholtz rollers and streamwise vortices found in previous studies. In the absence of stratification, the shear layer thickness grows linearly and fully developed turbulence is achieved with mean velocities, turbulence intensities, and turbulent kinetic energy budgets that agree well with previous experimental and numerical data. When buoyancy is included, the shear layer grows to an asymptotic thickness, and the corresponding bulk Richardson number, Ri(b), is within the range, 0.32 +/- 0.06, found in previous studies. The apparent scatter in the evolution of Ri(b) is shown to have a systematic dependence on Reynolds and Prandtl numbers. A detailed description of buoyancy effects on turbulence energetics, transport, and mixing is presented. The Reynolds shear stress, < u(1)(')u(3)(')>, is significantly reduced by buoyancy, thus decreasing the shear production of turbulence. Owing to buoyancy, gradients in the vertical direction tend to be larger than other gradients in the fluctuating velocity and density fields. However, this anisotropy of the gradients is lower when the Reynolds number increases. Coherent finger-like structures are identified in the density field at late time and their vertical extent obtained by a scaling analysis. (C) 2007 American Institute of Physics.