Inertial particles, i.e., small heavy particles, can inhomogeneously distribute and form clusters even in statistically homogeneous turbulence. When the Reynolds number of turbulence is sufficiently high so that coherent structures with various length and time scales coexist, particles form clusters by the action of the coherent structures when the particle velocity relaxation time is in the inertial-range time scales. In general, thus formed clusters are larger for larger Stokes numbers (the nondimensional relaxation time). We propose a method to objectively describe the particle cluster created by the action of coherent structures in the inertial range. For this purpose, we generalize the sweep-stick mechanism [S. Goto and J. C. Vassilicos, Phys. Rev. Lett. 100, 054503 (2008)] to express two-dimensional sheetlike clusters in terms of the coarse-grained acceleration field of turbulence. The generalized mechanism also predicts the thickness of the clusters, which depends on the particle relaxation time, the magnitude of acceleration gradients, and the lifetime of coherent flow structures. The direct numerical simulations of fully developed turbulence in a periodic cube with the Taylor-length Reynolds number being about 740 support the proposed mechanism.

• Received 31 August 2020
• Accepted 26 February 2021

DOI:https://doi.org/10.1103/PhysRevFluids.6.044605