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Stability of Relative Equilibria of Point Vortices on a Sphere and Symplectic Integrators

Marsden, J. E. and Pekarsky, S. and Shkoller, S. (1999) Stability of Relative Equilibria of Point Vortices on a Sphere and Symplectic Integrators. Nuovo cimento della Società italiana di fisica. C, 22C (6). pp. 793-802. ISSN 0390-5551.

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This paper analyzes the dynamics of N point vortices moving on a sphere from the point of view of geometric mechanics. The formalism is developed for the general case of N vortices, and the details are provided for the (integrable) case N = 3. Stability of relative equilibria is analyzed by the energy-momentum method. Explicit criteria for stability of different configurations with generic and non-generic momenta are obtained. In each case, a group of transformations is specied, such that motion in the original (unreduced) phase space is stable modulo this group. Finally, we outline the construction of a symplectic-momentum integrator for vortex dynamics on a sphere.

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Additional Information:© Società Italiana di Fisica, ricevutoNov 18,1998; approvato May6,1999. The authors would like to gratefully thank P. NEWTON, A. BLAOM, G. PATRlCK and T. RATIU for their helpful comments and advice on this and related work. Paper presented at the International Workshop on “Vortex Dynamics in Geophysical Flows”,Castro Marina (LE), Italy, 22-26 June 1998. The authors of this paper have agreed to not receive the proofs for correction.
Issue or Number:6
Classification Code:PACS: 92.l0.Lq -; 47.32 -; 47.32.Cc-; 01.30.Cc
Record Number:CaltechAUTHORS:20101015-153037123
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20444
Deposited By: Ruth Sustaita
Deposited On:30 Nov 2010 22:15
Last Modified:03 Oct 2019 02:10

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