Accurate Lagrangian stochastic model on homogeneous turbulence under two shear orientations

The paper reports a numerical modelisation of homogeneous and stratified turbulence under vertical and horizontal shear by way of Lagrangian stochastic model (LSM) versus Froude number. Vertical and horizontal shear (θ = 0 and θ = π/2) are adopted. First, a comparison of predictions by LSM with results of direct numerical simulation of Jacobitz (DNSJ) is carried out. Current results obtained by LSM demonstrate the existence of asymptotic equilibrium states for various parameters of the problem particularly for the horizontal shear. 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 is detected for growth rate, ratio kinetic energy to total energy and potential energy to total energy beyond τ = 40. For two shear orientations, results of normalized production and turbulence dissipation are comparable with different approaches for τ ≥ 70. Second, a comparative study of various thermal and dynamic parameters governing the considered problem for horizontal and vertical shear is performed versus Froude number. This study indicates that the LSM can present a significant contribution for numerical modelisation of stratified and homogeneous turbulence especially in the presence of a horizontal shear.