Scaling of multi-particle lagrangian statistics in direct numerical simulations

Basic results on the evolution of shape and size of three- and four-particle Lagrangian clusters are reported from direct numerical simulations at Taylor-scale Reynolds numbers between 90 and 400 in isotropic turbulence. At early times shape distortion by viscous effects is such that both the area and volume increase less rapidly than the two-particle separation. Later-time behavior is characterized by power-law increases and a self-similar shape distribution. Reynolds number effects are more prominent in measures of size than in shape parameters.