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Eigenvalue bounds for the Orr—Sommerfeld equation. Part 2

Published online by Cambridge University Press:  29 March 2006

Daniel D. Joseph
Daniel D. Joseph
Affiliation:
Department of Aeronautics and Engineering Mechanics, University of Minnesota
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Abstract

Rigorous estimates of amplification rates, wave speeds and sufficient conditions for linear stability are derived for the manifold of solutions of the Orr—Sommerfeld problem governing parallel motion in the boundary layer and in round pipes. The estimates for channel flow (part I) are improved and compared with numerical results for the neutral stability of Jeffery—Hamel flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 36 , Issue 4 , 19 May 1969 , pp. 721 - 734
Copyright
© 1969 Cambridge University Press

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References

Eagles, P. M. 1966 J. Fluid Mech. 24, 191.
Fox, J., Lessen, M. & Bhat, W. 1968 Phys. Fluids, 11, 1.
Fraenkel, L. E. 1963 Proc. Roy. Soc. A, 272, 406.
Gill, A. E. 1965 J. Fluid Mech. 21, 503.
Joseph, D. 1968 J. Fluid Mech. 33, 617.
Joseph, D. & Carmi, S. 1969 Quart. Appl. Math. 27.
Leite, R. J. 1959 J. Fluid Mech. 5, 81.
Lin, C. C. 1945 Quart. Appl. Math. 111, 117.
Orr, W. 1907 Proc. Roy. Irish Acad. 27, 1.
Reid, W. 1965 Basic Developments in Fluid Dynamics. New York: Academic.
Salwen, H. & Grosch, E. 1968 Bull. of Am. Phys. Soc. (Abstract), 13, 814.