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Fluctuations of thermodynamic variables in stationary compressible turbulence. (English) Zbl 1294.76183
Summary: A large database of new direct numerical simulations of forced compressible turbulence on up to \(2048^{3}\) 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.

MSC:
76F50 Compressibility effects in turbulence
76F55 Statistical turbulence modeling
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