An improved method for coherent structure identification based on mutual K-nearest neighbors

ABSTRACT The clustering algorithm based on mutual K-nearest neighbors (MKNN) is presented to identify coherent structures in complicated fluid flows, in order to analyze the mass mixing and transport. First, both trajectory similarity and spatial proximity are used to describe and measure the coherence between particles. These two identification criteria are frame-invariant since they are derived from the relative distances of particles. Then, the concept of mutual K-nearest neighbors is introduced further, and particles with the same cluster label are identified as coherent structures after the initialization and merging process of clusters, while incoherent regions consist of incoherent particles, which cannot form a mutual K-nearest neighbors relationship with other particles. Finally, the MKNN-based clustering algorithm is applied to three examples, realizing the identification and tracking of coherent structures. The identification results show that the MKNN-based clustering algorithm is robust to parameter K, and a higher threshold λ of cluster quantity will be helpful to identify the finer structures in flows. Moreover, spatial proximity performs better in vortex identification, and trajectory similarity is more suitable for elongated structures (jets) identification. Importantly, the method presented analyzes the evolutions of vortices in detail, including the generation, stretching, and merging processes. In summary, the MKNN-based clustering algorithm takes particle trajectories as input data, analyzes the evolution of relative distances between particles quantitatively, and carries out clustering analysis on particles according to trajectory similarity and spatial proximity. The combination of the MKNN-based clustering algorithm and frame-invariant identification criteria shows great potential in coherent structure identification of complicated fluid flows.