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arXiv · 1810.13364

Winding of a Brownian particle around a point vortex

Huanyu Wen·Jean-Luc Thiffeault
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Abstract

We derive the asymptotic winding law of 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 disk, 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.

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Huanyu Wen, Jean-Luc Thiffeault. 2018-10-31. Winding of a Brownian particle around a point vortex. https://doi.org/10.1098/rsta.2018.0347

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