A quasinormal scale elimination model of turbulent flows with stable stratification

A new spectral model for turbulent flows with stable stratification is presented. The model is based on a quasi-Gaussian mapping of the velocity and temperature fields using the Langevin equations and employs a recursive procedure of small-scale mode elimination that results in a coupled system of differential equations for effective, horizontal and vertical, viscosities and diffusivities. With increasing stratification, the vertical viscosity and diffusivity are suppressed while their horizontal counterparts are enhanced thus explicitly accounting for the anisotropy introduced by stable stratification. The new model is used to derive various spectral characteristics of stably stratified turbulent flows. It accounts for energy accumulation in the horizontal components at the expense of the energy reduction in the vertical component. The scale elimination algorithm explicitly accounts for the combined effect of turbulence and internal waves. A modified dispersion relation for internal waves, a relationship for internal wave frequency shift, and a threshold criterion for internal wave generation in the presence of turbulent scrambling are derived. It is shown how the model can be utilized to derive parameters needed for Reynolds-averaged Navier-Stokes modeling. Implemented in the K-ε format, the new model produces results that agree very well with the observational data on stably stratified atmospheric boundary layers and that are difficult to obtain using traditional two-equation turbulence modeling.