Winding of a Brownian particle around a point vortex
Probability
2020-01-16 v1 Fluid Dynamics
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.
Keywords
Cite
@article{arxiv.1810.13364,
title = {Winding of a Brownian particle around a point vortex},
author = {Huanyu Wen and Jean-Luc Thiffeault},
journal= {arXiv preprint arXiv:1810.13364},
year = {2020}
}
Comments
16 pages, 16 figures. SIAM LaTeX style