Accurate Lagrangian stochastic model on homogeneous turbulence under two shear orientations

Abstract

The paper reports a numerical modelization of thermal and dynamic characteristics of homogeneous and stratified turbulence under vertical and horizontal shear via Lagrangian Stochastic Model (LSM) for various Froude number ranging from 0.28 to 1.11. Two different orientations shear are defined by a vertical and a horizontal shear corresponding to θ = 0 and θ = π/2, respectively. Firstly, a comparison of predictions using a second order model of LSM to results via Direct Numerical Simulation of Jacobitz (DNSJ) (Jacobitz F (2002)) is carried out. It is found that present results obtained by LSM demonstrate the existence of asymptotic equilibrium states for various thermal and dynamic parameters of the problem in particularly for the case of horizontal shear (θ = π/2). Compared to the case of a vertical shear, an excellent agreement between predictions of LSM related to the case of horizontal shear and results of DNSJ (Jacobitz F (2002)) is detected for various parameters of growth rate, ratios kinetic energy to total energy and potential energy to total energy (γ, K/E, Kρ/E) beyond τ = 40. For two shear orientations, results of normalized production P/SK and turbulence dissipation ε/KS are comparable with different approaches at higher time 70 ≤ τ. Secondly, a comparative study between findings of different parameters (principal component of anisotropy b12, normalized production P/SK, normalized turbulence dissipation ε/KS, density flux [Formula: see text], ratio kinetic energy to total energy K/E and ratio of potential energy to total energy Kρ/E) governing the turbulence under horizontal and vertical shear is performed for different Froude number. The present study indicates that the LSM can present a significant contribution for numerical modelization related to problems of stratified and homogeneous turbulence especially in the presence of an horizontal shear.