Broken mirror symmetry of tracer's trajectories in turbulence

TL;DR

This paper demonstrates that the mean helicity in turbulent flows influences the topological linking of fluid trajectories, enabling experimental measurement of helicity through trajectory analysis and revealing long-term memory effects.

Contribution

It establishes a quantitative link between mean helicity and the linking number of Lagrangian trajectories, providing a new method to measure helicity experimentally.

Findings

Linking number depends on mean helicity

Trajectory links reveal long-term memory effects

Experimental measurement of mean helicity is possible

Abstract

Topological properties of physical systems play a crucial role in our understanding of nature, yet their experimental determination remains elusive. We show that the mean helicity, a dynamical invariant in ideal flows, quantitatively affects trajectories of fluid elements: the linking number of Lagrangian trajectories depends on the mean helicity. Thus, a global topological invariant and a topological number of fluid trajectories become related, and we provide an empirical expression linking them. The relation shows the existence of long-term memory in the trajectories: the links can be made of the trajectory up to a given time, with particles positions in the past. This property also allows experimental measurements of mean helicity.