A unifying framework for parameterizing stably stratified shear-flow turbulence

Abstract

An alternative framework for parameterizing stably stratified shear-flow turbulence is presented. Using dimensional analysis, four non-dimensional parameters of interest are identified that consider the independent effects of stratification, shear, viscosity, and scalar diffusivity. In the interest of geophysical applications, the problem is further simplified by considering only high Reynolds number flow. This leads to a two-dimensional parameter space based on a buoyancy strength parameter (i.e., an inverse Froude number) and a shear strength parameter. Consideration for the gradient Richardson number allows the space to be divided into an unforced regime, a shear-dominated regime, and a buoyancy-dominated regime. On this basis, a large database of direct numerical simulation and laboratory data from various sources is evaluated. Of particular interest is the observed length scale of overturning. Overturns are found to scale with k1/2/N in the buoyancy-dominated regime, k1/2/S in the shear-dominated regime, and k3/2/ε in the unforced regime, where k, N, S, and ε are the turbulent kinetic energy, buoyancy frequency, mean shear rate, and turbulent kinetic energy dissipation rate, respectively. Implications for estimates of diapycnal mixing in the ocean are discussed and a new parameterization for eddy diffusivity is presented.