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Fluctuations of thermodynamic variables in stationary compressible turbulence

Published online by Cambridge University Press:  23 September 2013

Diego A. Donzis  and
Shriram Jagannathan
Diego A. Donzis*
Affiliation:
Department of Aerospace Engineering, Texas A&M University, College Station, TX 12345, USA
Shriram Jagannathan
Affiliation:
Department of Aerospace Engineering, Texas A&M University, College Station, TX 12345, USA
*
†Email address for correspondence: donzis@tamu.edu
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Abstract

A large database of new direct numerical simulations of forced compressible turbulence on up to $204{8}^{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.

JFM classification

Turbulent Flows: Compressible turbulence Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 733 , 25 October 2013 , pp. 221 - 244
Copyright
©2013 Cambridge University Press 

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