A generalized Osborn–Cox model for estimating fluxes in nonequilibrium stably stratified turbulent shear flows

This paper describes a nonsteady state generalization of the Osborn–Cox formulas for estimating diapycnal fluxes from microstructure measurements in evolving ocean turbulence. The analysis is based on the same homogeneous turbulence assumption employed in the Osborn–Cox model, but the time dependent terms neglected in their analysis are retained. The analysis is greatly simplified by the finding from laboratory and numerical simulations that stably stratified homogeneous turbulence always evolves into a state of exponential growth or decay of turbulent kinetic and potential energies. Fluxes and diffusivities estimated using the present nonsteady state generalization can differ from Osborn–Cox estimates by as much as 50%, depending on the estimated growth rates. A scaling analysis leads to approximate analytical expressions for the growth rates of turbulent kinetic and potential energies. These dimensionless growth rates are functions of the gradient Richardson number, turbulence Reynolds number, and the kinetic and potential energy shear numbers, which can all be determined in principle from velocity and temperature microstructure measurements.