Regular and Chaotic Motion of Two-Dimensional Point Vortices

  • Y. Kimura
  • H. Hasimoto
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 30)

Abstract

A point vortex is a model of a real vortex with δ –function-type vorticity configuration in space. The equations of motion for N-point vortices in an unbounded region are given as follows:
$$\frac{{d{z_j}}}{{dt}} = \frac{1}{{2\pi i}}\sum\limits_{m = 1}^N {\frac{{{\Gamma _m}}}{{{{\bar z}_j} - {{\bar z}_m}}}} (j = 1,2, \cdots ,N)$$
(1)
where Zj (= xj+iyj) is a position of j-th vortex in the complex Z-plane, and Гj is its strength. The bar on the variable means that we take complex conjugate, and the prime denotes that we omit the singular terms j=m from the sum.

Keywords

Vortex Soliton Vorticity Lide Hongo 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Y. Kimura
    • 1
  • H. Hasimoto
    • 1
  1. 1.Department of Physics, Faculty of ScienceUniversity of TokyoHongo, Bunkyo Tokyo 113Japan

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