Point Vortices on the Sphere: Stability of Symmetric Relative Equilibria

Laurent-Polz, Frederic and Montaldi, James and Roberts, Mark (2011) Point Vortices on the Sphere: Stability of Symmetric Relative Equilibria. Journal of Geometric Mechanics, 3 (4). pp. 439-486. ISSN 1941-4897

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Abstract

We describe the linear and nonlinear stability and instability of certain symmetric configurations of point vortices on the sphere forming relative equilibria. These configurations consist of one or two rings, and a ring with one or two polar vortices. Such configurations have dihedral symmetry, and the symmetry is used to block diagonalize the relevant matrices, to distinguish the subspaces on which their eigenvalues need to be calculated, and also to describe the bifurcations that occur as eigenvalues pass through zero.

Item Type:	Article
Uncontrolled Keywords:	Hamiltonian systems, symmetry methods, bifurcations, momentum map, point vortices
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory MSC 2010, the AMS's Mathematics Subject Classification > 76 Fluid mechanics
Depositing User:	Dr James Montaldi
Date Deposited:	29 Mar 2011
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1594

Available Versions of this Item

• Stability of Relative Equilibria of Point Vortices on the Sphere. (deposited 02 Dec 2005)
  • Point Vortices on the Sphere: Stability of Symmetric Relative Equilibria. (deposited 29 Mar 2011) [Currently Displayed]

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