Variational necessary and sufficient stability conditions for inviscid shear flow
A necessary and sufficient condition for linear stability of inviscid parallel shear flow is formulated by developing a novel variational principle, where the velocity profile is assumed to be monotonic and analytic. It is shown that unstable eigenvalues of Rayleigh's equation (which is a non-s...
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Published in | Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Vol. 470; no. 2172; p. 20140322 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
England
The Royal Society Publishing
08.12.2014
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Subjects | |
Online Access | Get full text |
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Summary: | A necessary and sufficient condition for linear stability of inviscid parallel shear flow is formulated by developing a novel variational principle, where the velocity profile is assumed to be monotonic and analytic. It is shown that unstable eigenvalues of Rayleigh's equation (which is a non-self-adjoint eigenvalue problem) can be associated with positive eigenvalues of a certain self-adjoint operator. The stability is therefore determined by maximizing a quadratic form, which is theoretically and numerically more tractable than directly solving Rayleigh's equation. This variational stability criterion is based on the understanding of Kreĭn signature for continuous spectra and is applicable to other stability problems of infinite-dimensional Hamiltonian systems. |
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Bibliography: | istex:9ACEEF2813BF96E9FA71AE902FE372FED3A6FE86 ark:/67375/V84-ZWP05VD9-C ArticleID:rspa20140322 href:rspa20140322.pdf ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
ISSN: | 1364-5021 1471-2946 |
DOI: | 10.1098/rspa.2014.0322 |