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A new calculus for two-dimensional vortex dynamics

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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Author information

Correspondence to Darren Crowdy.

Additional information

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

Communicated by H. Aref

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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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Keywords

  • Two dimensional flow
  • Complex potential
  • Multiply connected

PACS

  • 47.15.ki
  • 47.15.km
  • 47.32.C