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A Kolmogorov-like exact relation for compressible polytropic turbulence

Published online by Cambridge University Press:  21 February 2014

Supratik Banerjee Open the ORCID record for Supratik Banerjee [Opens in a new window]  and
Sébastien Galtier
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Abstract

Compressible hydrodynamic turbulence is studied under the assumption of a polytropic closure. Following Kolmogorov, we derive an exact relation for some two-point correlation functions in the asymptotic limit of a high Reynolds number. The inertial range is characterized by: (i) a flux term implying in particular the enthalpy; and (ii) a purely compressible term $\mathcal{S}$ which may act as a source or a sink for the mean energy transfer rate. At subsonic scales, we predict dimensionally that the isotropic $k^{-5/3}$ energy spectrum for the density-weighted velocity field ($\rho ^{1/3} \boldsymbol {v}$), previously obtained for isothermal turbulence, is modified by a polytropic contribution, whereas at supersonic scales $\mathcal{S}$ may impose another scaling depending on the polytropic index. In both cases, it is shown that the fluctuating sound speed is a key ingredient for understanding polytropic compressible turbulence.

JFM classification

Turbulent Flows: Compressible turbulence Turbulent Flows: Homogeneous turbulence Turbulent Flows: Turbulence theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 742 , 10 March 2014 , pp. 230 - 242
Copyright
© 2014 Cambridge University Press 

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