Direct numerical simulations of isotropic compressible turbulence: Influence of compressibility on dynamics and structures

Abstract

In the present paper the statistical properties of compressible isotropic turbulence are analyzed by means of direct numerical simulations. The scope of the work is to evaluate the influence of compressibility on the time evolution of mean turbulence properties and to quantify the statistical properties of turbulent structures, their dynamics and similarities with the incompressible case. Simulations have been carried out at various turbulent Mach numbers and compressibility ratios by using a conservative hybrid scheme that relies on an optimized weighted essentially nonoscillatory approach for the convective terms and compact differencing for the viscous contributions. In order to identify similarities with incompressible turbulence we have also carried out an analysis in the plane of the second (Q*) and third (R*) invariants of the anisotropic part of the deformation rate tensor. The simulations show that the joint probability density function (Q*,R*) has a universal structure, as found in incompressible turbulence. The study confirms that the enstrophy obeys a two-stage evolution, due to the competing mechanisms of vortex stretching and viscous dissipation; however, at high turbulent Mach numbers, compressibility effects, associated to the occurrence of shocklets, become important. Furthermore, the analysis of the controlling mechanisms of vorticity generation has shown that even for compressible turbulence the growth of enstrophy is associated to a preferential alignment of the vorticity with the intermediate eigenvector of the anisotropic part of the strain-rate tensor.