Combination of Hierarchical Vortex Clustering with Liutex and Application to Ring Tone

Combination of Hierarchical Vortex Clustering (HVC) with Liutex is proposed. Vortical points are extracted by Liutex, a rigid rotation part of fluid motion, and these points are clustered into locally connected groups named p-cluster in the framework of HVC. Point clouds within vortical regions are obtained from an instantaneous flow field by employing a sequence of parallel planes oriented perpendicular to a specific direction. These point clouds are organized between successive planes and their cross-sectional distributions are aggregated along that direction. Each set of points is recognized as an individual entity termed a “p cluster,” with “p” replaced by descriptors such as proto, sub, super, and hyper, reflecting varying levels of clustering. The spatial distribution and temporal progression of these p clusters are then visualized and tracked automatically. The proposed method is applied to ring tone in which a small number of vortices hidden within numerous background vortices play an important role in producing the tone.