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Note on eigenvalue bounds for the Orr-Sommerfeld equation

Published online by Cambridge University Press:  29 March 2006

Chia-Shun Yih
Chia-Shun Yih
Affiliation:
Department of Engineering Mechanics, University of Michigan
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Abstract

Bounds for the complex wave velocity c, determined by the Orr-Sommerfeld equation and the boundary conditions for channel flow, have been given by Joseph (1968a,b). In these notes it is shown how two of Joseph's theorems can be uniformly improved.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 38 , Issue 2 , 3 September 1969 , pp. 273 - 278
Copyright
© 1969 Cambridge University Press

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References

Joseph, D. D. 1968 Eigenvalue bounds for the Orr-Sommerfeld equation J. Fluid Mech. 33, 617–621.Google Scholar
Joseph, D. D. 1969 Eigenvalue bounds for the Orr-Sommerfeld equation, Part 2 J. Fluid Mech. 36, 721–734.Google Scholar
Synge, J. L. 1938 Hydrodynamic stability Semicentenn. Publ. Am. Math. Soc. 2, 227–69.Google Scholar