Dynamics of two point vortices in the presence of a fixed vortex

The various trajectories exhibited by two mutually interacting point vortices of arbitrary non-zero circulations in the velocity field of a fixed point vortex is examined. The underlying dynamical system is categorized and studied based on the zero and non-zero values of the angular impulse. In each case, a phase plane analysis conducted on a transformed coordinate system to obtain a complete classification of the vortex motions and to characterize the behavior of the inter-vortex distance functions. Finally, The analytical predictions are verified numerically and illustrated for different sets of initial conditions and circulations.