Self-similar clustering of inertial particles and zero-acceleration points in fully developed two-dimensional turbulence

Clustering of inertial particles in fully developed two-dimensional inverse cascading turbulence occurs for all particle relaxation times ranging from an order of magnitude under the smallest eddy turnover time to an order of magnitude above the largest eddy turnover time. Particle voids and clusters are statistically self-similar over a finite range of scales within the inertial range and are explained in terms of coarse-grained vorticity and resonant eddies (for voids) and in terms of zero-acceleration points (for clusters). The clustering of inertial particles reflects the clustering of zero-acceleration points. Essential to both explanations is the sweeping of small eddies by large ones. An important implication is that particle clustering can be explicitly described just in terms of the fluid acceleration field without the need for Lagrangian particle integrations.