The motion of a point vortex through gaps in walls

New analytical techniques for studying the motion of a point vortex in fluid domains bounded by straight walls having an arbitrary number of gaps are presented. By exploiting explicit formulae for the Kirchhoff-Routh path function in multiply connected circular domains, combined with a novel construction of conformal mappings from such circular domains to multiply connected slit domains, the governing Hamiltonians for the motion of a point vortex in a number of physically interesting fluid regions involving walls with gaps are derived. The vortex trajectories in several illustrative cases are computed. These examples include finding the vortex paths around a chain of islands sitting off an infinite coastline, around islands in an unbounded ocean and around a sequence of islands Situated between two headlands.