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Accurate solution of the Orr–Sommerfeld stability equation

Published online by Cambridge University Press:  29 March 2006

Steven A. Orszag
Steven A. Orszag
Affiliation:
Department of Mathematics Massachusetts Institute of Technology
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Abstract

The Orr-Sommerfeld equation is solved numerically using expansions in Chebyshev polynomials and the QR matrix eigenvalue algorithm. It is shown that results of great accuracy are obtained very economically. The method is applied to the stability of plane Poiseuille flow; it is found that the critical Reynolds number is 5772·22. It is explained why expansions in Chebyshev polynomials are better suited to the solution of hydrodynamic stability problems than expansions in other, seemingly more relevant, sets of orthogonal functions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 50 , Issue 4 , 29 December 1971 , pp. 689 - 703
Copyright
© 1971 Cambridge University Press

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