DIRECT NUMERICAL SIMULATIONS OF THE TURBULENCE EVOLUTION IN A UNIFORMLY SHEARED AND STABLY STRATIFIED FLOW

Direct numerical simulations (DNS) are performed to investigate the ev olution of turbulence in a uniformly sheared and stably stratified flo w. The spatial discretization is accomplished by a spectral collocatio n method, and the solution is advanced in time with a third-order Rung e-Kutta scheme. The turbulence evolution is found to depend strongly o n at least three parameters: the gradient Richardson number Ri, the in itial value of the Taylor microscale Reynolds number Re-lambda, and th e initial value of the shear number SK/epsilon. The effect of each par ameter is individually studied while the remaining parameters are kept constant. The evolution of the turbulent kinetic energy K is found to follow approximately an exponential law. The shear number SK/epsilon, whose effect has not been investigated in previous studies, was found to have a strong non-monotone influence on the turbulence evolution. Larger values of the shear number do not necessarily lead to a larger value of the eventual growth rate of the turbulent kinetic energy. Var iation of the Reynolds number Re-lambda indicated that the turbulence growth rate tends to become insensitive to Ren at the higher end of th e Re-lambda range studied here. The dependence of the critical Richard son number Ri(cr), which separates asymptotic growth of the turbulent kinetic energy K from asymptotic decay, on the initial values of the R eynolds number Re-lambda and the shear number SK/epsilon was also obta ined. It was found that the critical Richardson number varied over the range 0.04 < Ri(cr) < 0.17 in our DNS due to its strong dependence on Reynolds and shear numbers.