Abstract
The effect of approximating a circular island of non-zero radius by a point dipole – the point island approximation – on the dynamics of two-dimensional vortices is studied. The approximation enables the Hamiltonian for N point vortices moving among M point islands to be derived. Examples of exact (within the point island approximation) trajectories for a single point vortex in domains involving gaps and multiple islands are presented. In addition, vortex patch motion using the point island approximation is computed numerically, demonstrating that such patches, provided they stay close to a circular shape, are well-modelled by point vortices. The effect of making the point island approximation on the trajectories of a point vortex about, (i), two islands and, (ii), an island within a gap, is investigated by comparing them to the exact trajectories in each case. It is found that the point island approximation is an efficient and accurate way of determining the behaviour of the vortex provided that the vortex and islands all remain well-separated in comparison to the vortex and island radii.
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