Path lengths in turbulence

TL;DR

This study investigates the geometric properties of particle trajectories in turbulent flows, revealing power-law scaling and distinguishing turbulence signatures through experimental and simulation comparisons.

Contribution

It introduces a detailed analysis of Lagrangian trajectory lengths and displacements in turbulence, highlighting their scaling behavior and turbulence signatures.

Findings

Displacement and total path length differ with power-law scaling.

Experimental results align with chaotic flow and stochastic models.

Results suggest a turbulence-specific geometric signature.

Abstract

By tracking tracer particles at high speeds and for long times, we study the geometric statistics of Lagrangian trajectories in an intensely turbulent laboratory flow. In particular, we consider the distinction between the displacement of particles from their initial positions and the total distance they travel. The difference of these two quantities shows power-law scaling in the inertial range. By comparing them with simulations of a chaotic but non-turbulent flow and a Lagrangian Stochastic model, we suggest that our results are a signature of turbulence.