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)


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:
$$\frac{{d{z_j}}}{{dt}} = \frac{1}{{2\pi i}}\sum\limits_{m = 1}^N {\frac{{{\Gamma _m}}}{{{{\bar z}_j} - {{\bar z}_m}}}} (j = 1,2, \cdots ,N)$$
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.


Chaotic Motion Singular Term Point Vortex External Flow Simple Shear Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H. Hasimoto, K. Ishii, Y. Kimura and M. Sakiyama: proc. IUTAM Symp. on Turbulence and Chaotic Phenomena in Fluids, Kyoto, 1983Google Scholar
  2. 2.
    C. C. Lin: Proc. Nat. Acad. Sci. USA 27, (1941), pp 570–575CrossRefGoogle Scholar
  3. 3.
    J. L. Synge: Can. J. Math. 1, (1949), pp 257–270CrossRefGoogle Scholar
  4. 4.
    H. Aref: Phys. Fluids 22, (1979), pp 393–400CrossRefGoogle Scholar
  5. 5.
    E. A. Novikov and Yu. B. Sedov: Sov. Phys. JETP 50, (1979), pp 297–301Google Scholar
  6. 6.
    D. V. Choodnovsky and G. V. Choodnovsky: IL NUOVO CIMENTO B 40 pp 339–353Google Scholar
  7. 7.
    Y. Ishimori: Prog. Theor. Phys. 72 (1), 1984, pp 33–37CrossRefGoogle Scholar

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

Personalised recommendations