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

The dynamics of a constrained three-vortex system, a pair of point vortices of arbitrary non-zero circulations in the velocity field of a fixed point vortex, is investigated. The underlying dynamical system is simplified using a coordinate transformation and categorized into two cases based on the zero and non-zero values of the constant of angular impulse. For each case, dynamical features of the vortex motion are studied analytically in the transformed plane to completely classify the vortex motions and understand the boundedness and periodicity of the inter-vortex distances. The theoretical predictions are also verified numerically and illustrated for various sets of initial conditions and circulations.