Zero-Noise Selection for Point Vortex Dynamics after Collapse

TL;DR

This paper explores how adding a tiny stochastic noise to point vortex systems affects their behavior after vortex collapse, resulting in a probabilistic description that preserves key conservation laws.

Contribution

It introduces a zero-noise regularization method that differs from deterministic approaches by producing a probability distribution of post-collapse trajectories.

Findings

Zero-noise regularization yields a probability distribution of trajectories.

The method preserves conservation laws of the vortex system.

It offers a new perspective on vortex dynamics after collapse.

Abstract

The continuation of point vortex dynamics after a vortex collapse is investigated by means of a regularization procedure consisting in introducing a small stochastic diffusive term, that corresponds to a vanishing viscosity. In contrast with deterministic regularization, in which a cutoff interaction selects in the limit a single trajectory of the system after collapse, the zero-noise method produces a probability distribution supported by trajectories satisfying relevant conservation laws of the point vortex system.