Homogeneous sheared stratified turbulence was simulated using a DNS code. The
initial turbulent Reynolds numbers (Re) were 22, 44, and 89, and the initial dimensionless
shear rate (S*) varied from 2 to 16. We found (similarly to Rogers (1986) for
unstratified flows) the final value of S* at high Re to be ∼ 11, independent of initial
S*. The final S* varies at low Re, in agreement with Jacobitz et al. (1997). At low Re,
the stationary Richardson number (Ris) depends on both Re and S*, but at higher
Re, it varies only with Re. A scaling based on the turbulent kinetic energy equation
which suggests this result employs instantaneous rather than initial values of flow
parameters.
At high Re the dissipation increases with applied shear, allowing a constant final S*.
The increased dissipation occurs primarily at high wavenumbers due to the stretching
of eddies by stronger shear. For the high-Re stationary flows, the turbulent Froude
number (Frt) is a constant independent of S*. An Frt-based scaling predicts the final
value of S* well over a range of Re. Therefore Frt is a more appropriate parameter for
describing the state of developed stratified turbulence than the gradient Richardson
number.