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Thermodynamical functions for a gas of point vortices

type de publication      article dans une revue internationale avec comité de lecture
date de publication 2008
auteur(s) Bécu Emilie; Pavlov Vadim; Tito Elizabeth P.
journal (abréviation) Compte-rendus Mécanique (Compt Rendus Mec)
volume (numéro) 336 (7)
  
pages 565 – 571
résumé We formulate nonlinear integro-differential equation for the averaged collective Hamiltonian of a gas of interacting two-dimensional vortices, derive its analytical solution, and discuss the equilibrium, axially-symmetrical, probability distributions that are possible for such a model. We also theoretically prove that the probability distribution for a system of 2D point vortices takes a form similar to the Gibbs distribution, but point out that the physical fundamentals of such a system differ from the standard theory of interacting particles. Furthermore, we find thermodynamical functions for positive and negative “temperature” of the system, and point out that the states with positive “temperature” correspond to stationary bell-shape vortex distributions, while the states with negative “temperature” correspond to distributions localized near container walls.
mots clés Dynamical systems; Hamiltonian description; Gas of localized vortices; Positive and negative “temperatures”
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