Hostname: page-component-848d4c4894-jbqgn Total loading time: 0 Render date: 2024-07-06T02:59:22.247Z Has data issue: false hasContentIssue false
  • English
  • Français

Equilibrium turbulent boundary layers

Published online by Cambridge University Press:  28 March 2006

G. L. Mellor  and
D. M. Gibson
G. L. Mellor
Affiliation:
Department of Aerospace and Mechanical Sciences, Princeton University
D. M. Gibson
Affiliation:
Department of Aerospace and Mechanical Sciences, Princeton University Present address: General Dynamics, Fort Worth, Texas.
Get access Rights & Permissions [Opens in a new window]

Abstract

Empirical information is extracted from constant-pressure flows and, on this basis alone, the equations of motion are solved for flows where the pressure gradient parameter, β = δ*(dp/dx)/τ0 is held constant. The experimental defect profiles of Clauser and the near-separating profile of Stratford are predicted quite well.

The present work is an extension of the work of Clauser and Townsend in that a particular form for an effective or eddy viscosity is hypothesized. Here, however, a continuous, and analytically precise family of defect profiles are calculated for the entire range, −0·5 ≤ β ≤ ∞. The solutions span the whole profile with the exception of the viscous sublayer.

A detailed consideration of the viscous sublayer and a comparative examination of various eddy viscosity hypotheses are included in a companion paper.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 24 , Issue 2 , February 1966 , pp. 225 - 253
Copyright
© 1966 Cambridge University Press

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

Clauser, F. 1954 Turbulent boundary layers in adverse pressure gradients. J. Aero. Sci. 21, 91–108.Google Scholar
Clauser, F. 1956 The turbulent boundary layer. Adv. Appl. Mech. 4, 1–51.Google Scholar
Coles, D. 1956 The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1, 191–226.Google Scholar
Coles, D. 1957 Remarks on the equilibrium turbulent boundary layer. J. Aero. Sci. 24, 495–506.Google Scholar
Gibson, D. M. & Mellor, G. L. 1962 Incompressible boundary layers in adverse pressure gradients. Mech. Eng. Rep., FLD 5, Princeton University.Google Scholar
Hartree, D. R. 1937 On an equation occurring in Falkner and Skan's approximate treatment of the equations of the boundary layer. Proc. Camb. Phil. Soc. 33, 223–39.Google Scholar
Hildebrand, F. B. 1949 Advanced Calculus for Engineers. New York: Prentice-Hall Inc.
Jeffries, H. 1962 Asymptotic Approximation. Oxford University Press.
Ludwig, H. & Tillman, W. 1950 Investigation of the wall shearing stress in turbulent boundary layers. NACA TM no. 1285.Google Scholar
Mellor, G. L. 1966 The effect of pressure gradients on the flow near a smooth wall. J. Fluid Mech., 24, 265.Google Scholar
Millikan, C. B. A. 1938 A critical discussion of turbulent flows in channels and circular tubes. Proc. Fifth Int. Congress Appl. Mech. pp. 386–92.Google Scholar
Rotta, J. 1950 Über die Theorie der tubulenten Grenzschichten, Mitt. Max-Planck-Inst., Gottingen, No. 1; translated as (1953): On the theory of the turbulent boundary layer. Nat. Adv. Comm. Aero., Wash., Tech. Mem. no. 1344.
Stratford, B. S. 1959a The prediction of separation of the turbulent boundary layer. J. Fluid Mech. 5, 1–16.Google Scholar
Stratford, B. S. 1959b An experimental flow with zero skin friction throughout its region of pressure rise. J. Fluid Mech. 5, 17–35.Google Scholar
Townsend, A. A. 1956 The properties of equilibrium boundary layers. J. Fluid Mech. 1, 561–73.Google Scholar
Townsend, A. A. 1960 The development of turbulent boundary layers with negligible wall stress. J. Fluid Mech. 8, 143–55.Google Scholar
Townsend, A. A. 1961 Equilibrium layers and wall turbulence. J. Fluid Mech. 11, 97–120.Google Scholar