Multi-particle and tetrad statistics in numerical simulations of turbulent relative dispersion

The evolution in size and shape of three and four-particle clusters (triangles and tetrads, respectively) in isotropic turbulence is studied using direct numerical simulations at grid resolution up to 4096(3) and Taylor-scale Reynolds numbers from 140 to 1000. A key issue is the attainment of inertial range behavior at high Reynolds number, while the small- and large-time limits of ballistic and diffusive regimes, respectively, are also considered in some detail. Tetrad size expressed by the volume (V) and (more appropriately) the gyration radius (R) is shown to display inertial range scaling consistent with a Richardson constant close to 0.56 for two-particle relative dispersion. For tetrads of initial size in a suitable range moments of shape parameters, including the ratio V-2/3/R-2 and normalized eigenvalues of a moment-of-inertia-like dispersion tensor, show a regime of near-constancy which is identified with inertial-range scaling. Sheet-like structures are dominant in this period, while pancakes and needles are more prevalent at later times. For triangles taken from different faces of each tetrad effects of the initial shape (isosceles right-angled or equilateral) are retained only for about one Batchelor time scale. In the inertial range there is a prevalence of nearly isosceles triangles of two long sides and one short side, representing one particle moving away from the other two which are still close together. In general, measures of shape display asymptotic scaling ranges more readily than measures of size. With some caveats, the simulation results are also compared with the limited literature available for multiparticle cluster dispersion in turbulent flow. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3586803]