Stability of Relative Equilibria of Point Vortices on the Sphere

Laurent-Polz, Frederic and Montaldi, James and Roberts, Mark (2005) Stability of Relative Equilibria of Point Vortices on the Sphere. [MIMS Preprint]

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Abstract

We describe the linear and nonlinear stability and instability of certain configurations of point vortices on the sphere forming relative equilibria. These configurations consist of up to two rings, with and without polar vortices. Such configurations have dihedral symmetry, and the symmetry is used both to block diagonalize the relevant matrices and to distinguish the subspaces on which their eigenvalues need to be calculated.

Item Type:	MIMS Preprint
Uncontrolled Keywords:	Hamiltonian systems, symmetry methods, momentum map
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:	02 Dec 2005
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/98

Available Versions of this Item

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

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