A hierarchical clustering method for volumetric vortical regions is proposed. Point clouds in vortical regions are extracted from an instantaneous flow field, using a series of parallel planes normal to a direction, and are grouped between consecutive planes. Cross-sectional distributions of points are then stacked in the direction. Each group of extracted points is identifiable as an individual entity that is referred to as a p cluster, with the letter p replaced by the terms proto, sub, super, and hyper, according to the level of clustering. The spatial distribution and temporal evolution of p clusters are visualized and automatically tracked. The present method is applied to the late stage of the K-type natural transition of a boundary-layer flow. Our method clearly captures, with admitting a detailed analysis, pairs of vortex structures located in the viscous sublayers near the roots of hairpin vortices. Moreover, it allows the algorithmic identification of dominant mathematical terms in the enstrophy and helicity equations, and a categorization of the extracted points based on local dynamics characterized by sets of the dominant terms. Construction of ensemble-averaged quantities using the present method, an extension of the method to omnidirections, and comparison between the present method and conventional vortex analysis methods are also discussed.
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