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2005.28: Stability of Relative Equilibria of Point Vortices on the Sphere

2005.28: Frederic Laurent-Polz, James Montaldi and Mark Roberts (2005) Stability of Relative Equilibria of Point Vortices on the Sphere.

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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 2000 > 37 Dynamical systems and ergodic theory
MSC 2000 > 76 Fluid mechanics
MIMS number:2005.28
Deposited By:Dr James Montaldi
Deposited On:02 December 2005

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