Direct numerical simulations of the turbulence evolution in a uniformly sheared and stably stratified flow

Abstract

Direct numerical simulations (DNS) are performed to investigate the evolution of turbulence in a uniformly sheared and stably stratified flow. The spatial discretization is accomplished by a spectral collocation method, and the solution is advanced in time with a third-order Runge–Kutta scheme. The turbulence evolution is found to depend strongly on at least three parameters: the gradient Richardson number Ri, the initial value of the Taylor microscale Reynolds number Reλ, and the initial value of the shear number SK/<ε. The effect of each parameter 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/<ε, 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. Variation of the Reynolds number Reλ indicated that the turbulence growth rate tends to become insensitive to Reλ at the higher end of the Reλ range studied here. The dependence of the critical Richardson number Ricr, which separates asymptotic growth of the turbulent kinetic energy K from asymptotic decay, on the initial values of the Reynolds number Reλ and the shear number SK/<ε was also obtained. It was found that the critical Richardson number varied over the range 0.04<Ricr<0.17 in our DNS due to its strong dependence on Reynolds and shear numbers.