A Reynolds Stress model with a new elliptic relaxation procedure for stratified flows

Abstract

The paper formulates a new derivation procedure for the standard elliptic relaxation turbulence model in the context of stratified flows. It begins with the introduction of an additional length scale for the buoyancy. A Taylor series expansion of the terms in the integral for the pressure-strain correlation paves the way for the formulation of an equivalent length scale as an explicit function of the integral length scale and the buoyancy length scale. The advantages of such an approach over previous research in the literature are two-fold: firstly, the number of elliptic relaxation equations is reduced by at least half thus making the model more practical and secondly, the same set of equations is valid for both stable and unstable stratification. The study forsakes elliptic relaxation for the scalar fluxes due to its emphasis on reducing computational complexity. The model predictions agree well with Direct Numerical Simulation (DNS) results available in the literature for both stably and unstably stratified flows at a range of stratification levels.