Chirality tomography: measuring local helicity from trajectory linking

TL;DR

This paper introduces chirality tomography, a novel Lagrangian method to map local helicity in turbulence by linking particle trajectory crossings to helicity density, revealing spatial heterogeneities and chiral structures.

Contribution

The paper presents the first 3D helicity maps from trajectory data, establishing a robust relation between trajectory linking and helicity, applicable to turbulent flows.

Findings

Helicity can be reconstructed from particle trajectories using signed crossings.

The method reveals spatial heterogeneities and chiral structures in turbulence.

The linking number correlates with helicity across different flow conditions.

Abstract

We present the first three-dimensional helicity maps of fully developed turbulence obtained through chirality tomography, a Lagrangian voxel-based method that reconstructs helicity density from particle trajectories. Our approach builds on an empirically established relation between helicity and trajectory linking, converting local counts of signed crossings $K$ into volumetric maps of dimensionless helicity, $H(\mathbf{x})$. We demonstrate that the entanglement of particle trajectories, quantified by the mean signed crossing number, provides a robust proxy for helicity, not only at the global scale, but also locally in space and time. Our method can reveal local spatial heterogeneities in helicity and relate them to large-scale flow organization, enabling the reconstruction of spatially resolved chiral structures. Applied to von K\'arm\'an experiments and Taylor-Green direct numerical simulations, the method reveals iso-helicity surfaces and coherent chiral features, while time series of $K$ accurately track the evolution of domain-averaged helicity. The proportionality between $K$ and $H$ remains robust across different voxel geometries and different values of particle inertia, but is not held in laminar or time-modulated flows. This study shows that chirality tomography provides a practical helicity diagnostic in turbulent flows, while establishing a direct bridge between trajectory-level topology and a fundamental dynamical invariant of turbulence.