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Kinetic theory of point vortices: diffusion coefficient and systematic drift

P. H. Chavanis
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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.

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BibTeXRIS

P. H. Chavanis. 2001-07-11. Kinetic theory of point vortices: diffusion coefficient and systematic drift. https://doi.org/10.1103/physreve.64.026309

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