Homogeneous sheared and stably stratified turbulence is considered as a fundamental flow relevant to the study of geophysical turbulence and, generally, anisotropic turbulence. Numerical experiments are performed via high resolution direct numerical simulation (DNS) in a geophysically-relevant parameter space previously inaccessible to simulation. Turbulent dynamics relevant to the modeling of geophysical hydrodynamics are investigated as a function of mean flow and fluid parameters. An active tuning scheme is implemented to induce temporally stationary turbulent kinetic energy in order to evaluate turbulence that is statistically independent of initial conditions and spatio-temporally homogeneous. Subject to this constraint, the parametric dependence of the flow reduces to a single Reynolds number, here defined as the shear Reynolds number Res ≡ (LC∕LK)4∕3 (Itweire et al. 1993, Corrsin 1958), where L C is the smallest turbulent anisotropic scale in the flow and LK represents the smallest scales of turbulence associated with viscosity, which parameterizes the range of length scales that are associated with isotropy for stationary flow configurations. By varying Res independently from other parameters, commonly suggested empirical scalings of the rate of mixing are shown to not hold. The turbulence and scalar dynamics approach an asymptotic state for Res ≿ 300, as evidenced by small-scale isotropy, an asymptotic partitioning of available potential energy to kinetic energy and two-point scaling. In light of this asymptotic state, an alternative parameterization is suggested, from robust classical scaling arguments, with dependence only on classical universal constants and mean energetics in the high Res limit. In an effort to simplify the conceptual description of geophysical turbulence, we suggest a unified length-scale framework based on the work of Gargett et al. 1984. Based on this framework, a parameterization for the isotropic length scale regime is suggested for generic (non-stationarity) flow configurations, which is evaluated with a series of decaying simulations.