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 ( Rλ ) and turbulent Mach ( Mₜ ) 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 Mₜ . The probability density functions (p.d.f.s) of pressure and density are negatively skewed at low Mₜ (consistent with incompressible results) but become positively skewed at high Mₜ . 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 Mₜ² . 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 Mₜ , 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.