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Scaling of global properties of turbulence and skin friction in pipe and channel flows

Published online by Cambridge University Press:  19 May 2010

VICTOR YAKHOT ,
SEAN C. C. BAILEY  and
ALEXANDER J. SMITS
VICTOR YAKHOT
Affiliation:
Department of Aerospace and Mechanical Engineering, Boston University, Boston, MA 02215, USA
SEAN C. C. BAILEY
Affiliation:
Department of Mechanical Engineering, University of Kentucky, Lexington, KY 40506, USA
ALEXANDER J. SMITS*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
*
†Email address for correspondence: asmits@princeton.edu
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Abstract

Experimental data on the Reynolds number dependence of the area-averaged turbulent kinetic energy K and dissipation rate ℰ are presented. It is shown that while in the interval ReD > 105 the total kinetic energy scales with friction velocity (K/u*2 = const), a new scaling law K/〈U〉2 ∝ K/(u*2ReDθ) = const (θ ≈ 1/4) has been discovered in the interval ReD < 105. It is argued that this transition is responsible for the well-known change in the scaling behaviour of the friction factor observed in pipe and channels flows at ReD ≈ 105.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 652 , 10 June 2010 , pp. 65 - 73
Copyright
Copyright © Cambridge University Press 2010

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References

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