Broken mirror symmetry of tracer's trajectories in turbulence

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.

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Cited by in corpus (3)

• Reconstructing velocity and pressure from sparse noisy particle tracks using Physics-Informed Neural Networks
• Clustering in laboratory and numerical turbulent swirling flows
• Multi-time structure functions and the Lagrangian scaling of turbulence