A Topological Framework for Flow Characterization and Identification

The characterization of complex flows is often based on kinetic and kinematic measurements computed from high dimensional sets of data. Computationally intensive processing of such large scale data sets is a major challenge in climatological and microfluidic applications. Here, we offer a novel approach 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 experimental video data with digital cameras and analyze the video frames with the isometric feature mapping (Isomap). We show that the topology of Isomap embedding manifolds directly captures inherent flow features without performing velocity measurements. 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.