Point vortices on the sphere: stability of relative equilibria

Details Point vortices on the sphere: stability of relative equilibria Point vortices on the sphere: stability of relative equilibria

2004-02-26

arxiv.org/abs/math/0402430v2

Mathematics

Dynamical Systems

47 pages, 40 figures

Scientific paper

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.

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