Interscale analysis of particle clusters amid turbulence*

The identification and tracking of clusters of loose, suspended particles in turbulent flows can be used to derive cluster statistics, determine cluster-dependent particle behavior, and understand the underlying turbulence (depending on the particle mass density). The formation of sediment clusters in coastal flows can cause optical occlusion, modulate the surrounding turbulence, and impact coral larvae settlement. The orientation of clusters relative to the mean flow can augment particle drag parameterizations. These loose clusters form, dissolve, and reshape just like dense particulate flocs agglomerate, break up, and restructure. Thus, statistics of loose particle clusters can shed light on the interscale nature of the underlying turbulence cascade. We apply an efficient number-density-based tree clustering method with basic similarities to DBSCAN to perform clustering for randomly distributed particles and particle-laden isotropic turbulence with near-unity Kolmogorov-scale Stokes numbers. Sensitivity of the power-law exponent of the cluster number distribution is reduced with appropriate choices of the proximity threshold and the minimum number of nearest neighbors per particle. Comparisons with the Voronoi and box-counting methods are performed. Individual particle tags are used to determine the continuity, breakup, and merger of particle clusters and evaluate particle fluxes along the phase-space coordinate of particle count to analyze interscale transport.