Finite-Reynolds-number effects in turbulence using logarithmic expansions

K. R. Sreenivasan, A. Bershadskii

Research output: Contribution to journalArticle

Abstract

Experimental or numerical data in turbulence are invariably obtained at finite Reynolds numbers whereas theories of turbulence correspond to infinitely large Reynolds numbers. A proper merger of the two approaches is possible only if corrections for finite Reynolds numbers can be quantified. This paper heuristically considers examples in two classes of finite-Reynolds-number effects. Expansions in terms of logarithms of appropriate variables are shown to yield results in agreement with experimental and numerical data in the following instances: The third-order structure function in isotropic turbulence, the mixed-order structure function for the passive scalar and the Reynolds shear stress around its maximum point. Results suggestive of expansions in terms of the inverse logarithm of the Reynolds number, also motivated by experimental data, concern the tendency for turbulent structures to cluster along a line of observation and (more speculatively) for the longitudinal velocity derivative to become singular at some finite Reynolds number. We suggest an elementary hydrodynamical process that may provide a physical basis for the expansions considered here, but note that the formal justification remains tantalizingly unclear.

Original languageEnglish (US)
Pages (from-to)477-498
Number of pages22
JournalJournal of Fluid Mechanics
Volume554
DOIs
StatePublished - May 2006

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Reynolds number
Turbulence
turbulence
expansion
logarithms
number theory
Number theory
isotropic turbulence
Reynolds stress
shear stress
Shear stress
tendencies
scalars
Derivatives

ASJC Scopus subject areas

  • Mechanics of Materials
  • Computational Mechanics
  • Physics and Astronomy(all)
  • Condensed Matter Physics

Cite this

Finite-Reynolds-number effects in turbulence using logarithmic expansions. / Sreenivasan, K. R.; Bershadskii, A.

In: Journal of Fluid Mechanics, Vol. 554, 05.2006, p. 477-498.

Research output: Contribution to journalArticle

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