A model for turbulence in moderately stratified flows

Models based on the Reynolds-averaged Navier-Stokes (RANS) equations have successfully predicted turbulence in weakly stratified flows, but they require adjustment in more strongly stratified flows to account for the interaction between turbulence and internal waves. In contrast, rapid distortion theory (RDT), which strictly applies for infinite Richardson number, captures many features of the wave mode of strongly stratified flows. To develop a model for turbulence in the moderate stratification observed in many environmental flows, we incorporated aspects of RANS models into RDT and attempted to predict the results of laboratory experiments of homogeneous turbulence in a stratified flow. Using a turbulent viscosity and diffusivity computed from length and velocity scales of the turbulence did not reproduce the timing of the oscillations of the vertical density flux. The inadequacy of the turbulent viscosity approach suggests including nonlinear interactions in the model by following the approach of Kevlahan and Hunt (1997).