Configurations of point vortices on the sphere are considered in which all vortex velocities are zero. A sharp upper bound for the number of equilibria lying on a great circle is found, valid for generic circulations, and some unusual equilibrium configurations with a free real parameter are described. Equilibria of rings (vortices evenly spaced along circles of latitude) are also discussed. All equilibrium configurations of four vortices are determined.
Keywords:
point vortices, sphere, equilibrium
Citation:
O'Neil K. A., Equilibrium Configurations of Point Vortices on a Sphere, Regular and Chaotic Dynamics,
2008, Volume 13, Number 1,
pp. 1-8