Effective velocity created by a point vortex in two-dimensional hydrodynamics.
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, in a statistical sense, the velocity created by a point vortex is shielded by cooperative effects on a distance Lambda approximately n(-1/2), the intervortex separation. For R>>Lambda, the "effective" velocity decays as R-2 instead of the ordinary law R(-1) recovered for R<<Lambda. These results are similar to those obtained by Agekyan [Sov. Astron. 5, 809 (1962)] 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.
Chavanis
Pierre-Henri
PH
Laboratoire de Physique Quantique, UMR 5626 du CNRS, Université Paul Sabatier, F-31062 Toulouse Cedex 4, France.