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 Taylor-scale Reynolds numbers over the range of 140–650. Extrapolation to the large Reynolds number limit gives an asymptotic value for Richardson’s constant in the range g=0.55–0.57, depending on the functional form used to make the extrapolation.