Fg. Jacobitz et al., DIRECT NUMERICAL SIMULATIONS OF THE TURBULENCE EVOLUTION IN A UNIFORMLY SHEARED AND STABLY STRATIFIED FLOW, Journal of Fluid Mechanics, 342, 1997, pp. 231-261
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.