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Elliptical vortices and integrable Hamiltonian dynamics of the rotating shallow-water equations

Published online by Cambridge University Press:  26 April 2006

Darryl D. Holm
Darryl D. Holm
Affiliation:
Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, MS B284, Los Alamos, NM 87545, USA
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Abstract

The problem of the dynamics of elliptical-vortex solutions of the rotating shallow-water equations is solved in Lagrangian coordinates using methods of Hamiltonian mechanics. All such solutions are shown to be quasi-periodic by reducing the problem to quadratures in terms of physically meaningful variables. All of the relative equilibria - including the well-known rodon solution - are shown to be orbitally Lyapunov stable to perturbations in the class of elliptical-vortex solutions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 227 , June 1991 , pp. 393 - 406
Copyright
© 1991 Cambridge University Press

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Footnotes

With an Appendix by D. David and T. K. Ohsumi.

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