A review of the study on coherent structures in turbulence by the clustering method

The intrinsic randomness of turbulence requires that the study of coherent structures has to be from the statistical point of view. The data-based clustering method is a powerful tool to realize the deep integration of coherent structures and statistics. It makes each continuous region, i.e., an individual structure, as a statistical sample. In addition, the spatial-temporal tracking method based on the spatial overlap of individual structure between consecutive snapshots makes the evolution of individual structure during its lifetime also as a statistical sample. Thus, both the kinematics and dynamics of coherent structures can be statistically described. We reviewed the history of this method and introduced the progress on Reynolds stress structures, velocity streaks, and cascades with emphasis. These results suggest that the clustering method extraordinarily extended our understanding of turbulence compared with the traditional point-wise statistics. Further prospects are also provided for future research.