Abstract
We derive the asymptotic winding law for a Brownian particle in the plane subjected to a tangential drift due to a point vortex. For winding around a point, the normalized winding angle converges to an inverse Gamma distribution. For winding around a disc, the angle converges to a distribution given by an elliptic theta function. For winding in an annulus, the winding angle is asymptotically Gaussian with a linear drift term. We validate our results with numerical simulations.This article is part of the theme issue ‘Topological and geometrical aspects of mass and vortex dynamics’.
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Schedule a callMore From: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
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