Persistent homology of vortex-dominated flows behind oscillating plates

Experimental and computational studies of vortex-dominated flows have shown that changes in the topology of vortices, that is, their structure and arrangement, correlate with the forces exerted on objects immersed in the flow. Quantifying topology using the framework of persistent homology allows for a more-explicit analysis of correlations between the topology and force measurements, both in simulated and experimental flows. Additionally, persistent homology inherently addresses the multiscale nature of determining what is meant by ``topology'' of any particular fluid flow. We demonstrate multiple approaches to computing the persistent homology of Lagrangian locations of vortices from discrete vortex models and of Eulerian vorticity fields measured in vortex-shedding experiments. In those situations when both types of data are available, we show that either approach results in equivalent topological quantifiers. Finally, we show that time-variation of persistent homology correlates with time variation of measured drag forces. These results suggest that characterizing vortex topology via persistent homology is dynamically meaningful for the study of vortex-dominated fluid flows, therefore opening avenues for the use of persistent homology as an input for optimization, machine learning, and control of fluid flows.