Explicit algebraic Reynolds stresses and scalar fluxes for density-stratified shear flows

An explicit algebraic model for Reynolds stresses and active scalar turbulent fluxes is proposed for simply stratified, stable shear flows such as atmospheric boundary layers of estuaries, including buoyant effects due to density variations (temperature, salinity). Under equilibrium assumptions, these models lead to explicit functions of the gradient Richardson number Ri that model the damping of the eddy viscosity and eddy diffusivity coefficients. The present model is compared to other existing theoretical approaches, as well as experimental observations, with satisfactory agreement. The evolution of the turbulent Prandtl number as a function of Ri is correctly predicted and its neutral value is consistent with existing values in the literature. The behavior of the model predicts that internal waves are responsible for momentum diffusion at large Ri, consistently with recent publications. The properties of turbulence anisotropy are briefly investigated.