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In the present investigation, the evolution of homogeneous and stratified turbulence under a horizontal and a vertical shear is deliberate by coupled second-order model SSG-SL. This model is a result of a combination between the Speziale, Sarkar and Gatski model (SSG) and the Shih and Lumley model (SL). Horizontal shear and vertical shear are related to the angle between the shear and the vertical gradient of stratification; θ = π/2 and θ = 0, respectively. This study is performed for different values of Froude number Fr ranging from 0.35–1.11. The SSG-SL model confirms the asymptotic equilibrium states for various physical parameters governing the problem (b 12 , b 11 , ε/KS,, K/E and K ρ /E) for two shear orientations (θ = π/2 and θ = 0). A comparison between findings using the present coupled model of SSG-SL and those by Direct Numerical Simulation of Jacobitz (DNSJ) [Jacobitz F, Sarkar S. A direct numerical study of transport and anisotropy in a stably stratified turbulent flow with uniform horizontal shear. Flow Turbul Combust. 2000;63:343–360.; Jacobitz F. A comparison of the turbulence evolution in a stratified fluid with vertical or horizontal shear. J Turbul. 2002;3:1–18.] is carried out. For the horizontal shear related to θ = π/2, an excellent agreement between predictions by the SSG-SL model and the results of DNSJ [Jacobitz, Sarkar;Jacobitz] is detected for turbulent thermal and dynamic fields.

Effect of the Froude number on a stratified turbulence under two shear orientations using coupled SSG and SL models