Probing the shape of turbulence through Lagrangian holographic vorticimetry

Turbulence is often perceived through a phenomenological lens, characterized by a chain of interacting vortices with energy cascading from large to small scales. However, traditional studies of turbulence rely on statistical averaging and stochastic dynamics due to the challenges in consistently tracking and quantifying the fast-evolving structures in turbulence. In this study, we present Lagrangian Holographic Vorticimetry (LHV) as an experimental approach to geometrically probe turbulence from the integral scale down to the Kolmogorov scale. Using LHV, we simultaneously track the translation and rotation of Kolmogorov-scale tracers, examining turbulence through changes in geometric properties such as deflection, rotation, and twist of the "ribbon" defined by the velocity and vorticity vectors. These properties are observed as tracers moving from one scale to another, characterized by surges in vorticity strength associated with encounters between tracers and high-vorticity filament regions in turbulence. Furthermore, by averaging these properties across different scales along the tracer trajectories, we provide a detailed geometric representation of scale similarities involved in the energy cascade within turbulence.