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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.
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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

Information

Type
Research Article
Information
Mathematika , Volume 28 , Issue 1 , June 1981 , pp. 116 - 140
Copyright
Copyright © University College London 1981

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