Holtsmark distributions in point-vortex systems
The statistics of uncorrelated point vortices in a plane is studied analytically and numerically. Theoretical distributions are obtained with the general method developed by Holtsmark [Ann. Phys. 58, 577 (1919)] and Chandrasekhar [Rev. Mod. Phys. 15, 1 (1943)]. They are found to agree with the results of numerical tests. Randomly placed Euler vortices have nearly Gaussian velocity distributions and Lorentzian distributions of the velocity difference. Statistics of other types of point vortices is essentially non-Gaussian.
Kuvshinov
BN
FOM Instituut voor Plasmafysica "Rijnhuizen," Associatie Euratom-FOM, Trilateral Euregio Cluster, P.O. Box 1207, 3430 BE Nieuwegein, The Netherlands.
Schep
TJ