On the modeling of homogeneous turbulence in a stably stratified flow

Abstract

The decay of incompressible, homogeneous turbulence in a stably stratified medium is investigated. A conventional high-Reynolds-number, two-equation model with suitable improvements for buoyancy effects is used to calculate the velocity field, while an explicit algebraic heat-flux model that depends on the velocity field and the transport of the temperature variance and its dissipation rate is invoked for the temperature field. The model thus derived could account for buoyancy flux and streamwise heat transport correctly and is used to investigate the decay of grid generated turbulence in a stably stratified medium. This class of flows displays countergradient transport of the vertical turbulent heat flux. Flows with buoyancy frequencies ranging from 0 to 2.42 are calculated. The results are compared with experimental data as well as with the calculations of a constant turbulent Prandtl number model, an algebraic-flux model and a second-order closure. The present model is found to be capable of correctly reproducing the countergradient heat transport phenomenon and the turbulence decay characteristics over the range of buoyancy frequency studied. However, the countergradient heat transport region is not captured by the algebraic flux and the constant turbulent Prandtl number model. Furthermore, the present results are in good agreement with data and with the predictions of a second-order closure.