Prediction of stably stratified homogeneous shear flows with second-order turbulence models

Abstract

The present study investigated the role of pressure-correlation second-order turbulence modelling schemes on the predicted behaviour of stably stratified homogeneous vertical-sheared turbulence. The pressure-correlation terms were modelled with a nonlinear formulation (Craft 1991), which was compared with a linear pressure–strain model and the ‘isotropization of production’ model for the pressure–scalar correlation. Two additional modelling issues were investigated: the influence of the buoyancy term in the kinetic energy dissipation rate equation and the time scale in the thermal production term in the scalar variance dissipation equation. The predicted effects of increasing the Richardson number on turbulence characteristics were compared against a comprehensive set of direct numerical simulation databases. The linear models provide a broadly satisfactory description of the major effects of the Richardson number on stratified shear flow. The buoyancy term in the dissipation equation of the turbulent kinetic energy generates excessively low levels of dissipation. For moderate and large Richardson numbers, the term yields unrealistic linear oscillations in the shear and buoyancy production terms, and therefore should be dropped in this flow (or at least their coefficient cε3 should be substantially reduced from its standard value). The mechanical dissipation time scale provides marginal improvements in comparison to the scalar time scale in the production. The observed inaccuracy of the linear model in predicting the magnitude of the effects on the velocity anisotropy was demonstrated to be attributed mainly to the defective behaviour of the pressure-correlation model, especially for stronger stratification. The turbulence closure embodying a nonlinear formulation for the pressure-correlations and specific versions of the dissipation equations failed to predict the tendency of the flow to anisotropy with increasing stratification. By isolating the effects of the dissipation rate equations, it was demonstrated that nonlinear closure provides an improved account of the normal components of the anisotropy tensor over the linear model; however, the vertical velocity correlation and the shear stress still present too large a discrepancy. The observed shortcomings may be intrinsic to the current structure of the pressure-correlation terms. None of the models were able to predict the ultimate collapse of the turbulent fluxes and counter-gradient fluxes. However, this weakness may be beyond the modelling of the redistribution processes, but instead in fundamental shortcomings in the energy dissipation rate equations and the dissipation tensor to adequately represent the phenomenology of the transition from shear- to buoyancy-dominated flows.