A Quasi-Normal Scale Elemination theory of turbulent flows with stable stratification

Abstract

A new spectral model of turbulent flows with stable stratification is presented. The theory is based upon a mapping of the actual velocity field to a quasi-Gaussian field using the Langevin equation. The parameters of the mapping are calculated using a systematic process of successive averaging over small shells of velocity and temperature modes that eliminates them from the equations of motion. The model predicts various important characteristics of stably stratified flows, such as the dependence of the vertical turbulent Prandtl number on Froude and Richardson numbers, anisotropization of the flow filed, and decay of vertical diffusivity under strong stratification, all in good agreement with computational and observational data. The theory also yields analytical expressions for various 1D and 3D kinetic and potential energy spectra that reflect the effects of waves and anisotropy. The model's results are suitable for immediate use in practical applications.