Virial theorem for Onsager vortices in two-dimensional hydrodynamics
Laboratoire de Physique Théorique (IRSAMC), Université de Toulouse, F-31062, Toulouse, France
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Revised: 17 October 2012
Accepted: 16 November 2012
Published online: 21 December 2012
We derive the virial theorem appropriate to two-dimensional point vortices at statistical equilibrium in the microcanonical and canonical ensembles. In an unbounded domain, it relates the angular velocity to the angular momentum and the temperature. Our expression is valid for an arbitrary number of point vortices of possibly different species. In the single-species case, and in the mean field approximation, it reduces to the relation empirically obtained by J.H. Williamson (J. Plasma Phys. 17, 85 (1977)).
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2012