Using braids to quantify interface growth and coherence in a rotor-oscillator flow

TL;DR

This paper explores the use of braid theory to estimate interface growth and coherence in fluid flows from sparse trajectory data, comparing experimental results with theoretical models to assess the method's effectiveness.

Contribution

It demonstrates the application of braid methods to experimental rotor-oscillator flow data and compares these with model predictions, highlighting both potential and challenges.

Findings

Braid methods can identify coherent regions in experimental flow data.

Interface growth rates show similar qualitative trends between experiment and model.

Quantitative differences indicate challenges in applying braid techniques to real data.

Abstract

The growth rate of material interfaces is an important proxy for mixing and reaction rates in fluid dynamics, and can also be used to identify regions of coherence. Estimating such growth rates can be difficult, since they depend on detailed properties of the velocity field, such as its derivatives, that are hard to measure directly. When an experiment gives only sparse trajectory data, it is natural to encode planar trajectories as mathematical braids, which are topological objects that contain information on the mixing characteristics of the flow, in particular through their action on topological loops. We test such braid methods on an experimental system, the rotor-oscillator flow, which is well-described by a theoretical model. We conduct a series of laboratory experiments to collect particle tracking and particle image velocimetry data, and use the particle tracks to identify regions of coherence within the flow that match the results obtained from the model velocity field. We then use the data to estimate growth rates of material interface, using both the braid approach and numerical simulations. The interface growth rates follow similar qualitative trends in both the experiment and model, but have significant quantitative differences, suggesting that the two are not as similar as first seems. Our results shows that there are challenges in using the braid approach to analyze data, in particular the need for long trajectories, but that these are not insurmountable.