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The aim of this work is to investigate the behavior of the Turbulent Prandtl number by second order modeling of a stably stratified homogeneous sheared turbulence. By analytic solutions, we have confirmed the asymptotic equilibrium behavior of the turbulent Prandtl number. Then two between the most second order models of turbulence; the Classic Launder-Reece-Model and the sophisticated Craft Launder model are retained. A non dimensional form of transport equations have been obtained when non dimensional parameters are introduced to substitute second order moments. A numerical integration using the fourth order Runge kutta method has been conducted for different values of the gradient Richardson number Ri. In comparison with direct numerical simulation result’s of Shih et al. the obtained results by the Craft Launder model has shown for the turbulent Prandtl number the best agreement at moderate values of gradient Richardson number 0.15 < Ri < 0.28. The classic model has shown a great default for the different values of Ri. No any concordance with retained results of DNS has been obtained by this model. We show also that prediction of this model can be improved by introducing variation and optimization of model constants.

ON THE TURBULENT PRANDTL NUMBER IN STABLY STRATIFIED TURBULENCE BY SECOND ORDER MODELS