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

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 Re λ , 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 Re λ indicated that the turbulence growth rate tends to become insensitive to Re λ at the higher end of the Re λ range studied here. The dependence of the critical Richardson number Ri cr , which separates asymptotic growth of the turbulent kinetic energy K from asymptotic decay, on the initial values of the Reynolds number Re λ and the shear number SK /<ε was also obtained. 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.