On the equilibrium distribution of like-signed vortices in two dimensions

  • Igor Mezić
  • Inki Min
Kinetics And Statistics
Part of the Lecture Notes in Physics book series (LNP, volume 511)


We study the equilibrium statistics for a system of point vortices of different circulations in two-dimensions. We use the methods of Lundgren and Pointin [2] who have analyzed this problem in the past for vortices of the same strength. This necessitates the development of the probability density functions for each of the vortices. We find a power-law relationship between the probability distributions of vortices with different circulations. These distributions are verified numerically.


Probability Density Function Point Vortex Large Vortex Small Vortex Microcanonical Ensemble 
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  1. [1]
    W. J. A. Dahm, K. B. Southerland, K. A. Buch, (1991): Phys. Fluids A3(5), 1115.ADSGoogle Scholar
  2. [2]
    T. S. Lundgren and Y. B. Pointin, “Statistical mechanics of two-dimensional vortices”, (1977): J. Stat. Physics, 17(5) 323.CrossRefADSGoogle Scholar
  3. [3]
    A. Vincent and M. Meneguzzi, “The spatial structure and statistical properties of homogeneous turbulence” (1991): J. Fluid Mech. 225, 1.zbMATHCrossRefADSGoogle Scholar
  4. [4]
    J. B. Weiss and J. C. McWilliams, “Nonergodicity of point vortices” (1991): Phys Fluids A 3, 835.CrossRefADSMathSciNetGoogle Scholar
  5. [5]
    I. Mezić, “On the statistical properties of motion of point vortices” (1995): UCSB preprint.Google Scholar
  6. [6]
    D. Montgomery and G. Joyce, “Statistical mechanics of ‘negative temperature’ states”, (1993): Phys. Fluids 17, 1139, (1974).CrossRefADSMathSciNetGoogle Scholar
  7. [7]
    P. D. Koumoutsakos, Ph.D. thesis, California Institute of Technology.Google Scholar
  8. [8]
    I. A. Min, “Transport, stirring and mixing in two-dimensional vortex flows” (1994): Ph.D. Thesis, California Institute of Technology.Google Scholar
  9. [9]
    I. A. Min, I. Mezić, A. Leonard, “Lévy stable distributions for velocity and velocity difference in systems of vortex elements”, (1996): Phys. Fluids, 8(5), 1169–1180.zbMATHCrossRefADSMathSciNetGoogle Scholar
  10. [10]
    P. G. Saffman, “Vortex Interaction and Coherent Structures in Turbulence” (1981): Transition and turbulence Proceedings of a symposium conducted by the Mathematics Research Center, the University of Wisconsin-Madison, October 13–15, Richard E. Meyer, ed.Google Scholar

Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Igor Mezić
    • 1
  • Inki Min
    • 2
  1. 1.Department of Mechanical EngineeringUniversity of CaliforniaSanta BarbaraUSA
  2. 2.The Aerospace CorporationEl SegundoUSA

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