Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-27T22:29:03.563Z Has data issue: false hasContentIssue false
  • English
  • Français

The stability of the asymptotic suction boundary layer profile

Published online by Cambridge University Press:  26 February 2010

P. Baldwin
P. Baldwin
Affiliation:
Department of Engineering Mathematics, University of Newcastle upon Tyne.
Get access

Abstract

The stability equation of the asymptotic suction boundary layer profile, using a linear stability analysis, is transformed into a generalised hypergeometric equation. The solution of the stability problem may thus be written formally in terms of the relevant generalised hypergeometric functions. An asymptotic analysis is carried out on these functions for large values of the Reynolds number, and the asymptotic representation of the solutions shown to agree with that given by the usual Orr–Sommerfeld analysis.

Type
Research Article
Information
Mathematika , Volume 17 , Issue 2 , December 1970 , pp. 206 - 242
Copyright
Copyright © University College London 1970

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

Abramowitz, M. and Stegun, I. A., Handbook of mathematical functions (Dover, 1965).Google Scholar
Barnes, E. W., Proc. London Math. Soc. (2), 5 (1907), 59–116.CrossRefGoogle Scholar
Grohne, D., Eine Lösung der Stabilitäts-differentialgleichung durch Laplace―Integrate in Sonderfall des asymptotischen Absaugeprofils, Ph.D. Thesis Max Planck-Institut Gottingen. 1950.Google Scholar
Heading, J., An introduction to phase-integral methods (Methuen, 1962).Google Scholar
Hughes, T. H. and Reid, W. H., J. Fluid Mech., 23 (1965), 715–735.CrossRefGoogle Scholar
Joseph, D. D., J. Fluid Mech., 36 (1969), 721–734.CrossRefGoogle Scholar
Kakutani, T., J. Phys. Soc. Japan, 19 (6), (1964), 1041–1057.CrossRefGoogle Scholar
Lock, R. C., Proc. Roy. Soc. Lond., A, 233 (1955), 105–122.Google Scholar
Olver, F. W. J., Proc. Camb. Phil. Soc., 48 (1952), 414–427.CrossRefGoogle Scholar
Olver, F. W. J., Phil. Trans. Roy. Soc., A, 247 (1955), 328–368.Google Scholar
Reid, W. H., In Basic developments in fluid mechanics, Vol. 1 (edited by Holt, M.), (1965), 249–307.Google Scholar
Squire, H. B., Proc. Roy. Soc. Lond., A, 142 (1933), 621–628.Google Scholar
Synge, J. L., Proc. Roy. Soc Lond., A, 167 (1938), 250–256.Google Scholar
Wasow, W., Annals Math., 58 (1953), 222–252.CrossRefGoogle Scholar
Wasow, W., J. Res. Nat. Bur. Standards, 51 (1953), 195–202.CrossRefGoogle Scholar
Watson, G. N., Trans. Camb. Phil. Soc., 22 (1913), 15–37.Google Scholar
Watson, G. N., A treatise on the theory of Bessel functions, 2nd edition (Cambridge, 1966).Google Scholar
Whittaker, E. T. and Watson, G. N., A course of modern analysis, 4th edition (Cambridge, 1965).Google Scholar
Wright, E. M., J. Lond. Math. Soc., 10 (1935), 287–293.Google Scholar
Wright, E. M., Proc. Lond. Math. Soc. (2), 46 (1940), 389–408.CrossRefGoogle Scholar