Coherent Structure Detection using Topological Tools and a Graph Theoretic Approach
For general aperiodic fluid flows, coherent structures help organize the dynamics. The prevalence of such flows in nature and industry has motivated many successful techniques for defining and detecting coherent structures. However, these approaches often require very fine trajectory data to reconstruct velocity fields. Instead, we use topological techniques to detect coherent trajectory sets in relatively sparse two-dimensional fluid advection problems. More specifically, we use a homotopy-based algorithm, the ensemble-based topological entropy calculation (E-tec), which evolves fluid material curves forward in time as minimal length bands stretched about the moving data points. These bands are represented as the weighted edges of a triangulation, which allows us to analyze flows using graph theory. In this way, highly connected components of appropriately constructed graphs can be used to partition the fluid particles into coherent trajectory sets.
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