Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-20T08:41:38.989Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Clauser, F. H. 1956 the trurbulent boundary layer. Adv. Mech. 4, 1–51.Google Scholar
Coles, D. E. 1956 The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1, 191–226.CrossRefGoogle Scholar
Coles, D. E. & Hirst, E. A. 1969 Compiled data. In Proc. Computation of Turbulent Boundary Layers, Vol. II. AFOSR-IFP-Stanford Conference 1968.Google Scholar
George, W. K. 2007 Is there a universal log law for turbulent wall-bounded flows? Phil. Trans. R. Soc. A 365, 789–806.CrossRefGoogle Scholar
George, W. K. & Castillo, L. 1997 Zero-pressure-gradient turbulent boundary layer. Appl. Mech. Rev. 50 (12), 689–729.CrossRefGoogle Scholar
Monkewitz, P. A., Chauhan, K. A. & Nagib, H. M. 2007 Self-consistent high-reynolds-number asymptotics for zero-pressure-gradient turbulent boundary layers. Phys. Fluids 19, 115101.CrossRefGoogle Scholar
Perry, A. E., Henbest, S. M. & Chong, M. S. 1986 A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165, 163–199.CrossRefGoogle Scholar
Perry, A. E., Marusic, I. & Jones, M. B. 2002 On the streamwise evolution of turbulent boundary layers in arbitrary pressure gradients. J. Fluid Mech. 461, 61–91.CrossRefGoogle Scholar
Rotta, J. C. 1962 Turbulent boundary layers in incompressible flow. Prog. Aero. Sci. 2, 1–219.CrossRefGoogle Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd Edn.Cambridge University Press.Google Scholar