Jason Hackl

Reynolds number dependence of relative dispersion statistics in isotropic turbulence

Direct numerical simulation results for a range of relative dispersion statistics over Taylor-scale Reynolds numbers up to 650 are presented in an attempt to observe and quantify inertial subrange scaling and, in particular, Richardson’s t3 law. The analysis includes the mean-square separation and a range of important but less-studied differential statistics for which the motion is defined relative to that at time t=0. It seeks to unambiguously identify and quantify the Richardson scaling by demonstrating convergence with both the Reynolds number and initial separation. According to these criteria, the standard compensated plots for these statistics in inertial subrange scaling show clear evidence of a Richardson range but with an imprecise estimate for the Richardson constant. A modified version of the cube-root plots introduced by Ott and Mann [J. Fluid Mech. 422, 207 (2000)] confirms such convergence. It has been used to yield more precise estimates for Richardson’s constant g which decrease with Taylo...

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 40963 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 V2/3/R2 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 ne...