A Study of the Asymptotic Equilibrium Behavior in Stratified Turbulence Submitted to Horizontal Shear

In this work, the asymptotic equilibrium behaviour of dimensionless parameters in stably stratified turbulence submitted to a horizontal shear is studied using two different methods. The first one is an analytic method and is based on linear solutions obtained when non linear effects of pressure and viscosity are neglected. The Laplace Transform is used for integrating differential system. The principal result of this first part of our work is the existence of asymptotic equilibrium states at high shear for all non dimensionless parameters. The second method is a numerical one and is based on a second-order modeling of equations. The Speziale Sarkar and Gatski (SSG) model is retained for pressure-strain correlation and dissipation time evolution equation, whereas, three of the most known second-order models are retained for the scalar field. The principal result of this second part is the big contribution of the SSG models for predicting asymptotic equilibrium states of non dimensional parameters.