Thermodynamic behavior in decaying, compressible turbulence with initially dominant temperature fluctuations

Direct numerical simulation of decaying, isotropic, compressible turbulence in three dimensions is used to examine the behavior of fluctuations in density, temperature and pressure when the initial conditions include temperature fluctuations larger than pressure fluctuations. The numerical procedure is described elsewhere, the initial turbulent Mach number is subsonic, 0.3 to 0.7, and the initial compressible turbulence is characterized as being in one of three states in which the ratios of initial kinetic energy in the compressible modes to total kinetic energy are, respectively, very small, moderate or nearly unity. Only at the lowest values of initial turbulent Mach number and energy ratio do thermodynamic scalings follow the predictions in the literature. For turbulent Mach numbers above 0.3, or for finite values of the kinetic energy ratio, the scalings are more complex. A relationship between turbulent Mach number, compressible pressure and energy ratio, which has been proposed previously for isothermal problems, appears to hold, on average, for the cases computed in this study, all of which are non-isothermal.