Laboratory investigations of a chaotic flow using braid theory

Abstract

Describing transport in fluid flows has been a long-standing challenge in dynamical systems theory, with applications to industrial and natural flows. The detection of Lagrangian structures that stay coherent over time helps gain insight into the evolution of a system's dynamics and the fate of transport. Whereas most techniques to detect coherent structures rely on a dense velocity field, techniques based on sparse datasets are increasingly being developed. The braid theory approach to detect Lagrangian coherent structures from sparse sets of trajectories is tested through a periodic, two-dimensional Stokes flow, the rotor-oscillator flow. Combined theoretical and numerical studies have shown that this flow can offer chaotic regimes with islands of coherence. The flow was recreated experimentally in a laboratory based on the findings of these theoretical studies. The braid theory approach was found to successfully detect coherent groups from sparse trajectories, although it is very sensitive to the quality of that data available.