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On the asymptotic similarity of the zero-pressure-gradient turbulent boundary layer

Published online by Cambridge University Press:  10 December 2008

M. B. JONES ,
T. B. NICKELS  and
IVAN MARUSIC
M. B. JONES
Affiliation:
School of Mathematical Sciences, Queensland University of Technology, Australia
T. B. NICKELS
Affiliation:
Department of Engineering, Cambridge University, UK
IVAN MARUSIC*
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia
*
‡Email address for correspondence: imarusic@unimelb.edu.au
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Abstract

We investigate similarity solutions for the outer part of a zero-pressure-gradient turbulent boundary layer in the limit of infinite Reynolds number. Previous work by George (Phil. Trans. R. Soc. vol. 365, 2007 p. 789) has suggested that the only appropriate velocity scale for the outer region is U1, the free-stream velocity. This is based on the fact that scaling with U1 leads to a mathematically valid similarity solution of the momentum equation for the outer region in the asymptotic limit of infinite Reynolds number. Here we show that the classical scaling using the friction velocity also leads to a valid similarity solution for the outer flow in this limit. Therefore on this basis it is not possible to dismiss the friction velocity as a possible scaling as has been suggested by George (2007) and others. We show that both the free-stream velocity and the friction velocity are potentially valid scalings according to this theoretical criterion.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 616 , 10 December 2008 , pp. 195 - 203
Copyright
Copyright © Cambridge University Press 2008

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References

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