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A note on symmetry and stability for fluid flows

Chern, Shuh-Jye and Marsden, Jerrold E. (1990) A note on symmetry and stability for fluid flows. Geophysical and Astrophysical Fluid Mechanics, 51 (1-4). pp. 19-26. ISSN 0309-1929. doi:10.1080/03091929008219848.

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In this note it is shown that Andrews' theorem, which states that Arnol'd stability implies symmetry, is not special to fluid mechanics, but holds in the general context of classical mechanics with symmetry. More importantly, we emphasise that in Andrews' theorem one should consider stability modulo the symmetry group of solution class. We do this by using the energy-Casimir method to prove the stability of two-dimensional ABC flows, even though they are not symmetric.

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Additional Information:© 1990 Gordon and Breach, Science Puhlishers, Inc. Received 25 March 1989; in final form 28 June 1989. We thank Darryl Holm for a critical reading of the paper and the referee for some useful suggestions.
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG03-88ER-25064
MSI/Cornell UniversityUNSPECIFIED
Issue or Number:1-4
Record Number:CaltechAUTHORS:20100730-102210176
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19229
Deposited By: Ruth Sustaita
Deposited On:30 Jul 2010 17:44
Last Modified:08 Nov 2021 23:50

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