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.