The motion of a point vortex through gaps in walls

Abstract

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.