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

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

2001-09-19

arxiv.org/abs/cond-mat/0109352v1

Phys. Rev. E, 65, 056302 (2002)

Physics

Condensed Matter

Statistical Mechanics

Submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.65.056302

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.

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