基于聚类连通法的湍流拟序结构研究进展

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

湍流的无序性要求对拟序结构的研究必须从统计的角度出发,而聚类连通法(clustering method)则是实现拟序结构与统计方法深度融合的有力工具.该方法是一种基于数据的流动特征提取方法,它将每个连通域,即单个拟序结构作为一个统计样本.此外,其衍生的基于连通域空间重叠的时空追踪方法可以进一步研究这些结构的时空演化,该方法将每个拟序结构从生成到消亡的演化过程也视为统计样本,从而实现了对拟序结构运动学特征和动力学过程的统计刻画.本文回顾了聚类连通法的发展历程并着重介绍了人们采用该方法在雷诺切应力结构、速度条带和能量级串方面取得的重大进展,这些结果表明该方法极大拓展了人们基于传统的逐点统计方法对湍流的认识,因而具有很大的潜力.最后,对该方法在湍流中的应用给出了建议和展望.

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.