Subgrid effects on the filtered velocity gradient dynamics in compressible turbulence

Abstract

The subgrid effects on the dynamics of the filtered velocity gradient tensor (VGT) in compressible turbulence are studied by means of statistical analysis of the invariants of the filtered VGT in compressible mixing layers. The evolution of the filtered VGT is determined by the interaction among the invariants, the pressure effects, the viscous effects and the subgrid effects. Based on the probability fluxes in the plane of the second ( ) and the third ( ) invariants of the filtered VGT, it is found that the flux for the subgrid effect term changes most with the dilatation compared to the other terms. Further, a Schur decomposition of the filtered VGT into its normal part and non-normal part, which represent the local effect and the non-local effect of the flow dynamics, respectively, is used to deal with their effects of the velocity gradient. It is revealed that the compressibility is mainly related to the normal effect while the behaviour of the subgrid-scale (SGS) energy dissipation is mainly associated with the non-normal effect. A backscattering region of the SGS energy dissipation in the – plane is identified in the locally expanded regions, which is determined by the non-normal effect. Further, an SGS model with the non-local effect is proposed to give a better prediction of the SGS energy dissipation.