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Effects of shock topology on temperature field in compressible turbulence

Effects of two types of shock topology, namely, small-scale shocklet and large-scale shock wave, on the statistics of temperature in compressible turbulence were investigated by simulations. The shocklet and shock wave are caused by the solenoidal and compressive modes of driven forces, respectively. Hereafter, the related two flows are called as SFT and CFT, respectively. It shows that in SFT the temperature spectrum follows the k^-5/3 power law, and the temperature field has "ramp-cliff" structures. By contrast, in CFT the temperature spectrum obeys the k^-2 power law, and the temperature field is dominated by large-scale rarefaction and compression. The power-law exponents for the p.d.f. of large negative dilatation are -2.5 in SFT and -3.5 in CFT, close to theoretical values. For the isentropic assumption of thermodynamic variables, the derivation in SFT grows with the turbulent Mach number (Mt), and for same Mt, the variables in CFT are more anisentropic. The angle statistics shows that the temperature gradient in CFT is preferentially perpendicular to the anisotropic strain rate tensor. It tends to be parallel with the first eigenvector and be orthogonal with the other two eigenvectors. For the cascade of temperature, the temperature variance is increased by the viscous dissipation and the pressure-dilatation, but is decreased by the SGS temperature flux. The statistics of pressure-dilatation proves that the negligible contribution of pressure-dilatation at small scales is due to the cancelations of high values between rarefaction and compression regions. The strongly positive skewness of the p.d.f.s of pressure-dilatation implies that the conversion from kinetic to internal energy through compression is more intense than the opposite process through rarefaction. Furthermore, in SFT the fluctuations of pressure-dilatation approximately follow the Zeman model.