Kinetic theory of point vortices: diffusion coefficient and systematic drift.
We develop a kinetic theory for point vortices in two-dimensional hydrodynamics. Using standard projection operator techniques, 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.
Chavanis
P H
PH
Laboratoire de Physique Quantique, Université Paul Sabatier, 118 route de Narbonne 31062, Toulouse, France.