Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-30T20:26:39.718Z Has data issue: false hasContentIssue false
  • English
  • Français

Uniform asymptotic solutions of the orr–sommerfeld equation

Part of: Turbulence

Published online by Cambridge University Press:  26 February 2010

P. Baldwin
P. Baldwin
Affiliation:
Department of Engineering Mathematics, University of Newcastle upon TyneClaremont Road, Newcastle upon Tyne 2.
Get access

Summary

Reid (1974) derived “first approximations” to solutions of the Orr–Sommerfeld equation, which are uniformly valid in a full neighbourhood of a critical point. This paper shows that such approximations may be calculated to higher order, and makes a first step towards placing the theory on a rigorous basis by providing error bounds for the dominant-recessive approximations. These are obtained by generalizing methods discussed by Olver (1974) for second order linear ordinary differential equations.

MSC classification

Secondary: 76F10: Shear flows
Type
Research Article
Information
Mathematika , Volume 28 , Issue 1 , June 1981 , pp. 116 - 140
Copyright
Copyright © University College London 1981

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

Davey, A.. Quart. J Mech. Appl. Math., 26 (1973), 401–411.CrossRefGoogle Scholar
Davey, A.. J. Comp. Phys., 24 (1977), 331–338.CrossRefGoogle Scholar
Eagles, P. M.. Quart. J. Mech. Appl. Math., 22 (1969), 129–182.CrossRefGoogle Scholar
Heisenberg, W.. Ann. Phys. Lpz., 24 (1924), 577.CrossRefGoogle Scholar
Lakin, W. D., Ng, B. S. and Reid, W. H.. Phil. Trans. Roy. Soc. Lond., 289 (1978), 347–371.Google Scholar
Lin, C. C.. Quart. App. Math., 3 (1945), 117–142, 218–234, 277–301.CrossRefGoogle Scholar
Lin, C. C.. The Theory of Hydrodynamic Stability (Cambridge University Press, 1955).Google Scholar
Lin, C. C. and Rabenstein, A. L.. Trans. Amer. Math. Soc., 94 (1960), 24–57.Google Scholar
Lin, C. C. and Rabenstein, A. L.. Studies in Appl. Math., 49 (1970), 311–340.Google Scholar
Olver, F. W. J.. Asymptotics and Special Functions (Academic Press, 1974).Google Scholar
Reid, W. H.. Studies in Appl. Math., 51 (1972), 341–368.CrossRefGoogle Scholar
Reid, W. H.. Studies in Appl. Math., 53 (1974), 217–224.CrossRefGoogle Scholar
Stewartson, K. and Stuart, J. T.. J. Fluid Mech., 48 (1971), 529–545.CrossRefGoogle Scholar
Thomas, L. H.. Phys. Rev., 91 (1953), 780–783.CrossRefGoogle Scholar
Tollmien, W.. Nach. Ges. VHss. Gottingen, Math.-Phys. KL., (1929), 21–44.Google Scholar
Tollmien, W.. Agnew, Z.. Math. Mech., 25–27 (1947), 33–50 and 70–83.Google Scholar