Scaling and parameterization of stratified homogeneous turbulent shear flow

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 ( Fr t ) is a constant independent of S *. An Fr t -based scaling predicts the final value of S * well over a range of Re . Therefore Fr t is a more appropriate parameter for describing the state of developed stratified turbulence than the gradient Richardson number.