## 2006.246: Relative equilibria of point vortices on the sphere

2006.246:
Chjan Lim, James Montaldi and Mark Roberts
(2001)
*Relative equilibria of point vortices on the sphere.*
Physica D: Nonlinear Phenomena, 148.
pp. 97-135.
ISSN 0167-2789

Full text available as:

PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader 351 Kb |

DOI: 10.1016/S0167-2789(00)00167-6

## Abstract

We prove the existence of many different symmetry types of relative equilibria for systems of identical point vortices on a non-rotating sphere. The proofs use the rotational symmetry group SO(3) and the resulting conservation laws, the time-reversing reflectional symmetries in O(3), and the finite symmetry group of permutations of identical vortices. Results include both global existence theorems and local results on bifurcations from equilibria. A more detailed study is made of relative equilibria which consist of two parallel rings with n vortices in each rotating about a common axis. The paper ends with discussions of the bifurcation diagrams for systems of 3–6 identical vortices.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Point vortices; Symmetry; First integrals; Flow on a sphere |

Subjects: | MSC 2000 > 37 Dynamical systems and ergodic theory MSC 2000 > 70 Mechanics of particles and systems |

MIMS number: | 2006.246 |

Deposited By: | Ms Lucy van Russelt |

Deposited On: | 08 August 2006 |

Download Statistics: last 4 weeks

Repository Staff Only: edit this item