  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.
