Point vortices on the sphere: a case with opposite vorticities

Details Point vortices on the sphere: a case with opposite vorticities Point vortices on the sphere: a case with opposite vorticities

2001-09-25

arxiv.org/abs/math/0109202v1

Published in Nonlinearity (15), 143-172 (2002)

Mathematics

Dynamical Systems

35 pages, 9 figures

Scientific paper

10.1088/0951-7715/15/1/307

We study systems formed of 2N point vortices on a sphere with N vortices of strength +1 and N vortices of strength -1. In this case, the Hamiltonian is conserved by the symmetry which exchanges the positive vortices with the negative vortices. We prove the existence of some fixed and relative equilibria, and then study their stability with the ``Energy Momentum Method''. Most of the results obtained are nonlinear stability results. To end, some bifurcations are described.

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