Logarithmic scaling of turbulence in smooth- and rough-wall pipe flow

M. Hultmark, M. Vallikivi, S. C.C. Bailey, A. J. Smits

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114 Scopus citations


Measurements of the streamwise component of the turbulent fluctuations in fully developed smooth and rough pipe flow are presented over an unprecedented Reynolds number range. For Reynolds numbers Reτ > 20000, the streamwise Reynolds stress closely follows the scaling of the mean velocity profile, independent of the roughness, and over the same spatial extent. This observation extends the findings of a logarithmic law in the turbulence fluctuations as reported by Hultmark, Vallikivi & Smits (Phys. Rev. Lett., vol. 108, 2012) to include rough flows. The onset of the logarithmic region is found at a location where the wall distance is equal to ~100 times the Kolmogorov length scale, which then marks sufficient scale separation for inertial scaling. Furthermore, in the logarithmic region the square root of the fourth-order moment also displays logarithmic behaviour, in accordance with the observation that the underlying probability density function is close to Gaussian in this region.

Original languageEnglish (US)
Pages (from-to)376-395
Number of pages20
JournalJournal of Fluid Mechanics
StatePublished - Aug 10 2013

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


  • Shear layer turbulence
  • Turbulent boundary layers
  • Turbulent flows


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