On the asymptotic solution of the Orr–Sommerfeld equation by the method of multiple-scales-Reference-Cited by-同舟云学术

On the asymptotic solution of the Orr–Sommerfeld equation by the method of multiple-scales

Published:1968-10-16 Issue:1 Volume:34 Page:145-158
ISSN:0022-1120
Container-title:Journal of Fluid Mechanics
language:en
Short-container-title:J. Fluid Mech.

Author:

Tam K. Kuen

Abstract

The method of multiple-scales is used to obtain the asymptotic solution of the Orr–Sommerfeld equation. For the special case of a linear velocity profile, the solution so obtained agrees well with an approximation of the exact solution which is known. For the general case, transformations on both the dependent and independent variables are introduced to obtain a zeroth-order equation which differs from the inner equation studied so far. On the ground of the favourable comparison for the special case, the asymptotic solution constructed is expected to be uniformly valid.

Publisher

Cambridge University Press (CUP)

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Reference10 articles.

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2. Lin, C. C. 1955 The Theory of Hydrodynamic Stability .Cambridge University Press.

3. Mahony, J. J. 1962 J. Aust. Math. Soc. 2,440.

4. Lin, C. C. & Rabenstein, A. L. 1960 Tran. Am. Math. Soc. 94,24.

5. Langer, R. E. 1955 Duke Math. J. 22,525.

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