Coherent structure coloring: identification of coherent structures from sparse data using graph theory
This addresses the challenge of analyzing fluid flows with limited data, which is common in practical applications like particle tracking velocimetry, though it is an incremental improvement over prior graph-based methods.
The paper tackles the problem of detecting coherent structures from sparse Lagrangian flow trajectories in fluid mechanics, presenting a frame-invariant method based on graph theory that robustly identifies these structures using significantly less data than existing spectral methods.
We present a frame-invariant method for detecting coherent structures from Lagrangian flow trajectories that can be sparse in number, as is the case in many fluid mechanics applications of practical interest. The method, based on principles used in graph coloring and spectral graph drawing algorithms, examines a measure of the kinematic dissimilarity of all pairs of fluid trajectories, either measured experimentally, e.g. using particle tracking velocimetry; or numerically, by advecting fluid particles in the Eulerian velocity field. Coherence is assigned to groups of particles whose kinematics remain similar throughout the time interval for which trajectory data is available, regardless of their physical proximity to one another. Through the use of several analytical and experimental validation cases, this algorithm is shown to robustly detect coherent structures using significantly less flow data than is required by existing spectral graph theory methods.