Fluctuations of thermodynamic variables in stationary compressible turbulence

A large database of new direct numerical simulations of forced compressible turbulence on up to 20483 grids, and a range of Reynolds (R-lambda) and turbulent Mach (M-t) numbers, is analysed to study the scaling of pressure, density and temperature fluctuations. Small-perturbation analysis is used to study the scaling of variances, and different cross-correlations as well as spectra. Qualitative differences are observed between low and high M-t. The probability density functions (p.d.f.s) of pressure and density are negatively skewed at low M-t (consistent with incompressible results) but become positively skewed at high M-t. The positive tails are found to follow a log-normal distribution. A new variable is introduced to quantify departures from isentropic fluctuations (an assumption commonly used in the literature) and is found to increase as M-t(2). However, positive fluctuations of pressure and density tend to be more isentropic than negative fluctuations. In general, Reynolds number effects on single-point statistics are observed to be weak. The spectral behaviour of pressure, density and temperature is also investigated. While at low M-t, pressure appears to scale as k(-7/3) (k is the wavenumber) in the inertial range as in incompressible flows, a k(-5/3) scaling also appears to be consistent with the data at a range of Mach numbers. Density and temperature spectra are found to scale as k(-5/3) for a range of Mach numbers.