Kinetic theory of point vortices: diffusion coefficient and systematic drift
Abstract
We develop a kinetic theory for point vortices in two-dimensional hydrodynamics. Using standard projection operator technics, we derive a Fokker-Planck equation describing the relaxation of a ``test'' vortex in a bath of ``field'' vortices at statistical equilibrium. The relaxation is due to the combined effect of a diffusion and a drift. The drift is shown to be responsible for the organization of point vortices at negative temperatures. A description that goes beyond the thermal bath approximation is attempted. A new kinetic equation is obtained which respects all conservation laws of the point vortex system and satisfies a H-theorem. Close to equilibrium this equation reduces to the ordinary Fokker-Planck equation.
Cite
@article{arxiv.cond-mat/0107219,
title = {Kinetic theory of point vortices: diffusion coefficient and systematic drift},
author = {P. H. Chavanis},
journal= {arXiv preprint arXiv:cond-mat/0107219},
year = {2009}
}
Comments
50 pages. To appear in Phys. Rev. E