Marsden, J.E. and Pekarsky, S. and Shkoller, S. (1999) Stability of relative equilibria of point vortices on a sphere and symplectic integrators. Il nuovo cimento C, 22 C (6). pp. 793-802. ISSN 1826-9885
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Abstract
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 N43. 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 specified, 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.
| Item Type: | Article |
|---|---|
| Additional Information: | Paper presented at the International Workshop on “Vortex Dynamics in Geophysical Flows”, Castro Marina (LE), Italy, 22-26 June 1998. |
| Uncontrolled Keywords: | Turbulence and diffusion ; Rotational flow and vorticity ; Vortex dynamics ; Conference proceedings |
| Subjects: | 500 Scienze naturali e Matematica > 550 Scienze della Terra > 551 Geologia, Idrologia, Meteorologia |
| Depositing User: | Marina Spanti |
| Date Deposited: | 11 Oct 2019 14:56 |
| Last Modified: | 11 Oct 2019 14:56 |
| URI: | http://eprints.bice.rm.cnr.it/id/eprint/13670 |
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