Velocity statistics for non-uniform configurations of point vortices

Abstract

Within the point vortex model, we compute the probability distribution function of the velocity fluctuations induced by same-signed vortices scattered within a disk according to a fractal distribution of distances to origin $\sim r^{-\alpha }$. We show that the different random configurations of vortices induce velocity fluctuations that are broadly distributed, and follow a power-law tail distribution, $P(V)\sim V^{\alpha -2}$ with a scaling exponent determined by the $\alpha$ 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 $\alpha$ of the vortex density distribution.

9 pages, 5 figures

References in corpus (4)

• Velocity Statistics Distinguish Quantum Turbulence from Classical Turbulence
• Inverse Energy Cascade in Forced 2D Quantum Turbulence
• Energy spectra of vortex distributions in two-dimensional quantum turbulence
• Vortex clustering and universal scaling laws in two-dimensional quantum turbulence

Cited by in corpus (5)

• Giant Vortex Clusters in a Two-Dimensional Quantum Fluid
• Theory of the vortex-clustering transition in a confined two-dimensional quantum fluid
• Origin of the inverse energy cascade in two-dimensional quantum turbulence
• Classical analogies for the force acting on an impurity in a Bose-Einstein condensate
• Velocity statistics for point vortices in the local α-models of turbulence