Interaction of a point vortex with boundary singularities of higher orders (Q1316785)

The motion of a point vortex in the field of a multipole, especially a dipole, situated at a rigid boundary surface and representing a localized liquid jet, is described based on the equations for the complex potentials of vortex and multipole in two-dimensional flow of a perfect fluid. The vortex dynamics is determined by a Hamiltonian system of equations, using polar coordinates. Since the so-called Hamiltonian itself does not depend explicitly on the time, the vortex trajectories are level lines of the Hamiltonian. There exist two types of vortex motion, whether the vortex comes from infinity and encounters the dipole jet or whether the vortex approaches the dipole jet from the rear. Both types of motion are discussed in detail.