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Exact Relation for Correlation Functions in Compressible Isothermal Turbulence

TitleExact Relation for Correlation Functions in Compressible Isothermal Turbulence
Publication TypeJournal Article
Year of Publication2011
AuthorsGaltier, S, Banerjee, S
JournalPhysical Review Letters
Volume107
Date PublishedSep
ISBN Number0031-9007
Accession NumberWOS:000298320900001
Abstract

Compressible isothermal turbulence is analyzed under the assumption of homogeneity and in the asymptotic limit of a high Reynolds number. An exact relation is derived for some two-point correlation functions which reveals a fundamental difference with the incompressible case. The main difference resides in the presence of a new type of term which acts on the inertial range similarly as a source or a sink for the mean energy transfer rate. When isotropy is assumed, compressible turbulence may be described by the relation -2/3 epsilon(eff) r =F(r)(r), where F(r) is the radial component of the two-point correlation functions and epsilon(eff) is an effective mean total energy injection rate. By dimensional arguments, we predict that a spectrum in k(-5/3) may still be preserved at small scales if the density-weighted fluid velocity rho(1/3) is used.

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