Thermodynamical functions for a gas of point vortices |
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Authors: | Emilie Bcu Vadim Pavlov Elizabeth P Tito |
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Institution: | aLaboratoire de mécanique de Lille – UMR 8107, 59655 Villeneuve d'Ascq cedex, France;bUFR de mathématiques pures et appliquées, Université de Lille 1, 59655 Villeneuve d'Ascq cedex, France;cCalifornia Institute of Technology, Pasadena, CA 91125, USA |
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Abstract: | 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. To cite this article: E. Bécu et al., C. R. Mecanique 336 (2008). |
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