2D/3D Topological data analysis of vortex dominated flows

Persistent homology (PH) is a topological data analysis (TDA) technique used to decipher complex data by detecting and tracking topological features. We apply methods of PH to the vortex wakes generated by pitching and heaving flat plates as models of bio-inspired propulsion. Velocity fields from stereoscopic particle image velocimetry are analyzed using Cubical PH with an effort to determine if there exists a relationship between the topological connectivity of the field and its physical interaction. Results show that using TDA to analyze these flow field interactions identifies vortex cores and boundaries as persistent features within their respective 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 its corresponding change in topology. Current work focuses on applying this method to 3D vortex flow data of rigid, bio-inspired trapezoidal pitching panels. Future work focuses on implementing other PH techniques, specifically zigzag persistence and multiparameter persistence to track persisting features through multidimensional analysis.