Kinetic theory of point vortices: diffusion coefficient and systematic drift

Details Kinetic theory of point vortices: diffusion coefficient and systematic drift Kinetic theory of point vortices: diffusion coefficient and systematic drift

2001-07-11

arxiv.org/abs/cond-mat/0107219v1

Phys. Rev. E, 64, 026309 (2001)

Physics

Condensed Matter

Statistical Mechanics

50 pages. To appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.64.026309

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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