Clustered Equilibria of Point Vortices

    2011, Volume 16, Number 6, pp.  555-561

    Author(s): O'Neil K. A.

    Point vortex equilibria in which the vortices are arranged in clusters are examined. The vortex velocities in these configurations are all equal. Necessary conditions for their existence are established that relate the circulations within the clusters to the cluster radius. A method for generating these configurations by singular continuation is proved to be valid for the generic case. Finally, a partial analysis of exceptional cases is given and their connection to the existence of parametrized families of equilibria is described.
    Keywords: point vortex, equilibrium, singular continuation
    Citation: O'Neil K. A., Clustered Equilibria of Point Vortices, Regular and Chaotic Dynamics, 2011, Volume 16, Number 6, pp. 555-561

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