A topological framework for flow characterization and identification

The characterization of complex flows is often based on ki-netic and kinematic measurements computed from high dimen-sional sets of data. Computationally intensive processing of such large scale data sets is a major challenge in climatological and microfluidic app lications. Here, we offer a novel app roach based on noninvasive and unsupervised analysis of fluid flows through nonlinear manifold learning. Specifically, we study varying flow regimes in the wake of a circular cylinder by acquiring exper-imental video data with digital cameras and analyze the video frames with the isometric feature mapp ing (Isomap). We show that the topology of Isomap embedding manifolds directly cap-tures inherent flow features without performing velocity measure-ments. Further, we establish relationships between the amount of embedded data and the Reynolds number, which are utilized to detect the flow regime of independent experiments.