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

Wirosoetisno, D. and Shepherd, T. G. ORCID: https://orcid.org/0000-0002-6631-9968 (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 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
URI	https://reading-clone.eprints-hosting.org/id/eprint/32848
Item Type	Article
Refereed	Yes
Divisions	No Reading authors. Back catalogue items Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
Publisher	American Institute of Physics
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