Decorrelating a compressible turbulent flow: an experiment

TL;DR

This experiment investigates the behavior of floating particles on turbulent fluid surfaces, measuring their information dimension and Lyapunov exponents, and compares results with theoretical models and simulations to understand their compressible dynamics.

Contribution

The study provides experimental measurements of information dimension and Lyapunov exponents for coagulated floaters, and introduces a novel analysis mimicking the Kraichnan ensemble.

Findings

Measured information dimension D_1 of floaters

Determined Lyapunov exponents of particle trajectories

Validated experimental results against theoretical models and simulations

Abstract

Floating particles that are initially distributed uniformly on the surface of a turbulent fluid, subsequently coagulate, until finally a steady state is reached. This being so, they manifestly form a compressible system. In this experiment, the information dimension D_1, and the Lyapunov exponents of the coagulated floaters, are measured. The trajectories and the velocity fields of the particles are captured in a sequence of rapidly acquired images. Then the velocity sequence is randomly shuffled in time to generate new trajectories. This analysis mimics the Kraichnan ensemble and yields properties of a velocity correlation function that is delta-correlated in time (but not in space). The measurements are compared with theoretical expectations and with simulations of Boffetta et al., that closely mimic the laboratory experiment reported here.