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A new calculus for two-dimensional vortex dynamics

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Abstract

This article provides a user’s guide to a new calculus for finding the instantaneous complex potentials associated with point vortex motion in geometrically complicated planar domains, with multiple boundaries, in the presence of background flows. The key to the generality of the approach is the use of conformal mapping theory together with a special transcendental function called the Schottky–Klein prime function. Illustrative examples are given.

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Authors and Affiliations

  1. Department of Mathematics, Imperial College London, 180 Queen’s Gate, London, SW7 2AZ, UK

    Darren Crowdy

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  1. Darren Crowdy
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Correspondence to Darren Crowdy.

Additional information

Communicated by H. Aref

In remembrance of Philip Geoffrey Saffman (1931–2008).

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Crowdy, D. A new calculus for two-dimensional vortex dynamics. Theor. Comput. Fluid Dyn. 24, 9–24 (2010). https://doi.org/10.1007/s00162-009-0098-5

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  • DOI: https://doi.org/10.1007/s00162-009-0098-5

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