On the effective velocity created by a point vortex in two-dimensional hydrodynamics

Abstract

We complete previous investigations on the statistics of velocity fluctuations arising from a random distribution of point vortices in two-dimensional hydrodynamics. We show that, on a statistical sense, the velocity created by a point vortex is shielded by cooperative effects on a distance $\Lambda \sim n^{-1/2}$, the inter-vortex separation. For $R\gg \Lambda$, the ``effective'' velocity decays as $R^{-2}$ instead of the ordinary law $R^{-1}$ recovered for $R\ll \Lambda$. These results are similar to those obtained by Agekyan [Sov. Astron. 5 (1962) 809] in his investigations on the fluctuations of the gravitational field. They give further support to our previous observation that the statistics of velocity fluctuations are (marginally) dominated by the contribution of the nearest neighbor.

Submitted to Phys. Rev. E

References in corpus (2)

• Kinetic theory of point vortices: diffusion coefficient and systematic drift
• Velocity field distributions due to ideal line vortices

Cited by in corpus (7)

• Kinetic theory of point vortices in two dimensions: analytical results and numerical simulations
• Dislocations Jam At Any Density
• Statistics of the gravitational force in various dimensions of space: from Gaussian to Levy laws
• Statistical mechanics of two-dimensional vortices and stellar systems
• Decay of Time Correlations in Point Vortex Systems
• Distribution Probability of Force for a Physical System of N Random Particles
• Dynamical aspects of spontaneous symmetry breaking in driven flow with exclusion