Multi-scale analyses of compressible turbulence 可压缩湍流的多尺度分析

Some recent studies on multi-scale properties of compressible turbulence conducted by the authors' group are reviewed. By multi-process decomposition methods, multi-scale properties of the solenoidal component, the dilatational component, the pseudo-sound mode, the acoustic mode, and the entropy modes of velocity and thermodynamic variables in compressible turbulence are studied. In addition, the scaling behaviors of spectra of velocity and thermodynamic variables in various situations of different compressibility are summarized. Inter-scale transfers of kinetic energy and thermodynamic variables are studied by filtering method, with the emphasis on the effects of compressibility on the inter-scale transfer of the dilatational component of kinetic energy. The compressible effects are stronger in compressible homogeneous shear turbulence. Mach number scaling behaviors of compressible kinetic energy and compressible dissipation rate are similar but have larger magnitudes as compared to those in compressible homogeneous isotropic turbulence. Distributions of eigenvalues of the strain rate tensor and the local flow topologies are more sensitive to the change of turbulent Mach number. For compressible isotropic turbulence in vibrational nonequilibrium, the vibrational relaxation between the translational-rotational and vibrational modes of internal energy results in the deviation between gradients of density and vibrational temperature, which further weakens the effect of compressibility on vibrational rate. Heat release through chemical reactions can greatly enhance compression and expansion motions and result in the increase of spectra of dilatational velocity components and thermodynamic variables at all length scales. The kinetic energy and its dissipation appear to be independent of the turbulent Mach number.