Kinetic energy transfer in compressible homogeneous anisotropic turbulence

Abstract

Numerical simulations of forced anisotropic turbulence (FAT) in a periodic box and homogeneous shear turbulence (HST) at various turbulent Mach (Ma${}_{\mathrm{T}}$) and Taylor Reynolds numbers are performed to study the anisotropy of kinetic energy (KE) transfer in compressible homogeneous turbulence. In both FAT and HST, the subgrid-scale KE flux is streamwise dominated at large scales, and tends to be isotropic at small scales. Using Helmholtz decomposition we find the FAT dilatational KE is nearly isotropic, but that of HST is significantly anisotropic. HST dilatational production increases monotonically with Ma${}_{\mathrm{T}}$, providing the main source of KE to the dilatational mode at high Ma${}_{\mathrm{T}}$.