The motion of a point vortex around multiple circular islands

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  • Darren G. Crowdy
    Imperial College of Science, Technology and Medicine Department of Mathematics, , 180 Queen’s Gate, London SW7 2AZ, United Kingdom
  • Jonathan S. Marshall
    Imperial College of Science, Technology and Medicine Department of Mathematics, , 180 Queen’s Gate, London SW7 2AZ, United Kingdom

Description

<jats:p>A new constructive method for computing the motion of a single point vortex around an arbitrary finite number of circular islands in the special case when the circulations around all the islands are zero is presented. In this case, explicit representations for the governing Hamiltonians can be found and used to study the vortex trajectories. An example application is to geophysical flows and this study provides a simple model of the interaction of ocean eddies with topography. A wide range of illustrative examples are given, including the case of various multi-island configurations lying off an infinite coastline as well as in an unbounded ocean. The critical trajectories (or separatrices) dividing the flow domain into regions of qualitatively different dynamics of the vortices can be computed in a systematic and unified fashion irrespective of the number of islands present.</jats:p>

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