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

Published online by Cambridge University Press:  11 July 2013

M. Hultmark ,
M. Vallikivi ,
S. C. C. Bailey  and
A. J. Smits
M. Hultmark*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
M. Vallikivi
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
S. C. C. Bailey
Affiliation:
Department of Mechanical Engineering, University of Kentucky, Lexington, KY 40506, USA
A. J. Smits
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA Monash University, Victoria 3800, Australia
*
†Email address for correspondence: [email protected]
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Abstract

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 $R{e}_{\tau } \gt 20\hspace{0.167em} 000$, 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.

JFM classification

Turbulent Flows: Shear layer turbulence Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 728 , 10 August 2013 , pp. 376 - 395
Copyright
©2013 Cambridge University Press 

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