Persistent homology of a bioinspired model fin vortex wake

Topology is a branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, i.e. without closing/opening holes, tearing, gluing, or passing through itself. We interpret the vorticity field of a bio-inspired pitching panel wake as a two dimensional set that has structure, or topology, that we wish to uncover. Specifically, we examine the efficacy of persistent homology (PH), a topological data analysis (TDA) technique used to decipher complex data by detecting and tracking topological features, within the field of fluid dynamics— a relatively new endeavor. Results show that using TDA to analyze these flow field sets identifies vortex cores and boundaries as persistent features by examining the H0 and H1 homology groups. Furthermore, metrics such as a bottleneck or Wasserstein distance provide a path for quantifying the significance of vortex shedding and the corresponding change in topology. This work investigates how the changes in flow field topology, as identified with PH, correspond to measured thrust production, time-averaged efficiency, and planform geometry for a range of bioinspired pitching panels.