On the existence of two-dimensional Euler flows satisfying energy-Casimir stability criteriaWirosoetisno, D. and Shepherd, T. G. (2000) On the existence of two-dimensional Euler flows satisfying energy-Casimir stability criteria. Physics of Fluids, 12 (3). pp. 727-731. ISSN 1070-6631 Full text not archived in this repository. It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1063/1.870280 Abstract/SummaryThe energy-Casimir stability method, also known as the Arnold stability method, has been widely used in fluid dynamical applications to derive sufficient conditions for nonlinear stability. The most commonly studied system is two-dimensional Euler flow. It is shown that the set of two-dimensional Euler flows satisfying the energy-Casimir stability criteria is empty for two important cases: (i) domains having the topology of the sphere, and (ii) simply-connected bounded domains with zero net vorticity. The results apply to both the first and the second of Arnold’s stability theorems. In the spirit of Andrews’ theorem, this puts a further limitation on the applicability of the method. © 2000 American Institute of Physics.
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