Stably Stratified Shear Turbulence: A New Model for the Energy Dissipation Length Scale

Abstract

A model is presented to compute the turbulent kinetic energy dissipation length scale l? in a stably stratified shear flow. The expression for l? is derived from solving the spectral balance equation for the turbulent kinetic energy. The buoyancy spectrum entering such equation is constructed using a Lagrangian timescale with modifications due to stratification. The final result for l? is given in algebraic form as a function of the Froude number Fr and the flux Richardson number Rf, l? = l?(Fr, Rf). The model predicts that for Rf < Rfc, l? decreases with stratification or shear; for Rf > Rfc, which may occur in subgrid-scale models, l? increases with stratification. An attractive feature of the present model is that it encompasses, as special cases, some seemingly different models for l? that have been proposed in the past by Deardorff, Hunt et al., Weinstock, and Canuto and Minotti. An alternative form for the dissipation rate ? is also discussed that may be useful when one uses a prognostic equation for the heat flux. The present model is applicable to subgrid-scale models, which are needed in large eddy simulations (LES), as well as to ensemble average models. The model is applied to predict the variation of l? with height z in the planetary boundary layer. The resulting l? versus z profile reproduces very closely the nonmonotonic profile of l? exhibited by many LES calculations, beginning with the one by Deardorff in 1974.