Velocity statistics for nonuniform configurations of point vortices.

Abstract

Within the point-vortex model, we compute the probability distribution function of the velocity fluctuations induced by same-sign vortices scattered within a disk according to a fractal distribution of distances to the origin ∼r^{-α}. We show that the different random configurations of vortices induce velocity fluctuations that are broadly distributed and follow a power-law tail distribution P(V)∼V^{α-2} with a scaling exponent determined by the α exponent of the spatial distribution. We also show that the range of the power-law scaling regime in the velocity distribution is set by the mean density of vortices and the exponent α of the vortex density distribution.