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Eigenvalue bounds in linear inviscid stability theory

Published online by Cambridge University Press:  11 April 2006

Alex D. D. Craik
Alex D. D. Craik
Affiliation:
Department of Applied Mathematics, University of St Andrews, Fife, Scotland
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Abstract

New eigenvalue bounds are derived for the linear stability of inviscid parallel flows, both for homogeneous and for stratified fluids. The usefulness of these bounds, as compared with that of previous results, is assessed for several examples. For homogeneous fluids the new upper bounds for the imaginary part ci of the complex phase velocity are sometimes better than previous criteria. For both homogeneous and stratified flows, the new upper bounds for the wave-number α of neutrally stable disturbances improve on previous results, giving values within 10% of the known exact solution in several cases.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 53 , Issue 4 , 27 June 1972 , pp. 657 - 670
Copyright
© 1972 Cambridge University Press

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References

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