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Boundary layers with small departures from the Falkner-Skan profile

Published online by Cambridge University Press:  28 March 2006

K. K. Chen  and
Paul A. Libby
K. K. Chen
Affiliation:
Department of the Aerospace and Mechanical Engineering Sciences, and the Institute for Pure and Applied Physical Sciences, University of California, San Diego, La Jolla, California
Paul A. Libby
Affiliation:
Department of the Aerospace and Mechanical Engineering Sciences, and the Institute for Pure and Applied Physical Sciences, University of California, San Diego, La Jolla, California
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Abstract

The description of a laminar boundary layer with a constant pressure gradient parameter β but with an initial velocity profile close to that given by the solution of the Falkner-Skan equation for that β, is shown to lead to an eigenvalue problem in much the same manner as prevails for the Blasius solution. However, it is found that only for β > β0, where β0 corresponds to the separation value, and for the upper branch solutions are the eigenvalues all positive and the flow spatially stable. The lower branch solutions involve negative as well as positive eigenvalues and are spatially unstable.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 33 , Issue 2 , 12 August 1968 , pp. 273 - 282
Copyright
© 1968 Cambridge University Press

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References

Bellman, R. 1963 Nonlinear Differential Equations and Nonlinear Mechanics (J. P. LaSalle and S. Lipschitz, Eds.). New York: Academic Press.
Ince, E. L. 1956 Ordinary Differential Equations, pp. 231–35. New York: Dover Publications.
Kalaba, R. 1963 Nonlinear Differential Equations and Nonlinear Mechanics (J. P. LaSalle and S. Lipschitz, Eds.). New York: Academic Press.
Libby, P. A. 1965 AIAA J. 3, 2164.
Libby, P. A. 1966 Int. J. Heat Mass Transfer, 9, 1109.
Libby, P. A. & Fox, H. 1963 J. Fluid Mech. 17, 433.
Libby, P. A. & Liu, T. M. 1967 AIAA J. 5, 1040.
Rosenhead, L. 1963 Laminar Boundary Layers. Oxford University Press.
Serrin, J. 1967 Proc. Roy. Soc. A. 299, 491.
VAN DYKE, M. 1964a Perturbation Methods in Fluid Mechanics. New York: Academic Press.
VAN DYKE, M. 1964b J. Fluid Mech. 19, 145.
Whittaker, E. T. & Watson, G. N. 1936 A Course in Modern Analysis (4th ed.). Cambridge University Press.