Turbulent Mixing in Stably Stratified Shear Flows

Abstract

Vertical mixing of momentum and heat is investigated in turbulent stratified shear flows. It is assumed that the flow has uniform shear and stratification with homogeneous turbulence and that an equilibrium is reached between kinetic and potential energy without gravity wave oscillations. A simple model is derived to estimate vertical diffusivities for Richardson numbers in between 0 and about 1. The model is based on the budgets of kinetic and potential energy and assumes a linear relationship between dissipation, shear, and vertical velocity variance for closure. Scalar fluctuations are related to shear or buoyancy frequency depending on the Richardson number. The turbulent Prandtl number and the growth rate of kinetic energy are specified as functions of this number. Model coefficients are determined mainly from laboratory measurements. Data from large-eddy simulations are used to determine the "stationary" Richardson number with balanced shear production, dissipation, and buoyancy terms. The results of the model are compared with data from laboratory experiments in air or saltwater, with measurements in the atmospheric boundary layer and in the stable troposphere, and with results from the numerical simulations. The model interpolates the observations within the scatter of the data. Theanalysis shows intrinsic relationships between several mixing parameters.