Simulation of shear orientation effects on stably stratified homogeneous turbulence with RANS second-order modelling

Abstract

The paper investigates the ability of a differential second-order turbulence closure to predict the effects of shear directionality on stably stratified homogeneous turbulence. The study does not aim to propose new turbulence models but rather aims to provide a detailed examination of the behaviour of the turbulence closure from an extensive set of available direct numerical simulations (DNS) of homogeneous and stably stratified flows that have been subjected to non-vertical shear. The study disclosed several previously unknown features about the predicted behaviour of turbulence subjected to a mean shear gradient that makes an arbitrary angle with the plane of the temperature gradient (which is aligned with the gravitational acceleration vector) for a wide range of Ri numbers. The turbulence closure comprises transport equations for all of the components of the Reynolds stress tensor, the heat flux vector and for the dissipation rates of kinetic energy and temperature fluctuations. Further, an anisotropic dissipation tensor is considered. The results show that the model captures the impact on the turbulence growth rate of increasing the horizontal shear. The model yields more energetic turbulence levels with increasing orientation angle, and it predicts accurately the “critical” inclination angle. One of the most important findings is that the model is capable of estimating the critical Ri for both the vertical and the horizontal shear cases when a properly calibrated buoyancy term is included in the ϵ-equation. For both cases, the model predicts the same turbulent Froude number for critical Richardson number, in agreement with the DNS data. Moreover, the present model is able to predict the strong increase in the mixing efficiency parameter from the vertical shear to the horizontal shear cases, which was not achieved in previous studies. The model is sensitive to buoyancy damping of vertical velocity fluctuations, which ultimately lead to the overall decay of all of the velocity components. The comparison of the present predictions with rapid distortion theory (RDT) analysis attests the importance of non-linear processes in the approach to “sudden suppression” of turbulence. However, some concerns remain in the behaviour of the model. A major source of uncertainty relates to the anisotropy of Reynolds stresses. It was found that the observed departure in the prediction of anisotropies is not simply related to the accuracy of the pressure–strain redistribution, but the anisotropic dissipation modelling has a role to play in stratified flows.

Keywords:

• homogeneous shear turbulence
• Reynolds-averaged Navier–Stokes equations
• second-order modelling
• stratified turbulence
• non-vertical shear