Subgrid-scale effects in compressible variable-density decaying turbulence

Many turbulent flows are characterized by complex scale interactions and vorticity generation caused by compressibility and variable-density effects. In the large-eddy simulation of variable-density flows, these processes manifest themselves as subgrid-scale (SGS) terms that interact with the resolved-scale flow. This paper studies the effect of the variable-density SGS terms and quantifies their relative importance. We consider the SGS terms appearing in the density-weighted Favre-filtered equations and in the unweighted Reynolds-filtered equations. The conventional form of the Reynolds-filtered momentum equation is complicated by a temporal SGS term; therefore, we derive a new form of the Reynolds-filtered governing equations that does not contain this term and has only double-correlation SGS terms. The new form of the filtered equations has terms that represent the SGS mass flux, pressure-gradient acceleration and velocity-dilatation correlation. To evaluate the dynamical significance of the variable-density SGS effects, we carry out direct numerical simulations of compressible decaying turbulence at a turbulent Mach number of 0.3. Two different initial thermodynamic conditions are investigated: homentropic and a thermally inhomogeneous gas with regions of differing densities. The simulated flow fields are explicitly filtered to evaluate the SGS terms. The importance of the variable-density SGS terms is quantified relative to the SGS specific stress, which is the only SGS term active in incompressible constant-density turbulence. It is found that while the variable-density SGS terms in the homentropic case are negligible, they are dynamically significant in the thermally inhomogeneous flows. Investigation of the variable-density SGS terms is therefore important, not only to develop variable-density closures but also to improve the understanding of scale interactions in variable-density flows.