Relative equilibria of point vortices on the sphere

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

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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 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory MSC 2010, the AMS's Mathematics Subject Classification > 70 Mechanics of particles and systems
Depositing User:	Ms Lucy van Russelt
Date Deposited:	08 Aug 2006
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/447

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