Point vortices on the sphere: a case with opposite vorticities
Dynamical Systems
2009-11-07 v1 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.math/0109202,
title = {Point vortices on the sphere: a case with opposite vorticities},
author = {Frederic Laurent-Polz},
journal= {arXiv preprint arXiv:math/0109202},
year = {2009}
}
Comments
35 pages, 9 figures