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On the existence of two-dimensional Euler flows satisfying energy-Casimir stability criteria

Wirosoetisno, 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

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To link to this article DOI: 10.1063/1.870280

Abstract/Summary

The 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.

Item Type:Article
Refereed:Yes
Divisions:No Reading authors. Back catalogue items
Faculty of Science > School of Mathematical and Physical Sciences > Department of Meteorology
ID Code:32848
Publisher:American Institute of Physics

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