Reynolds number dependence of Lagrangian statistics in large numerical simulations of isotropic turbulence

Lagrangian statistics are reported from a direct numerical simulation database with grid resolution up to 20483 and Taylor-scale Reynolds number approximately 650. The approach to Lagrangian Kolmogorov similarity at high Reynolds number is studied using both the velocity structure function and frequency spectrum. A significant scaling range is observed for the latter which is consistent with recent estimates of 6 - 7 for the scaling constant C-0. In contrast to some previous results at low Reynolds number, the current results suggest that at high Reynolds number the dissipation autocorrelation is a two-scale process influenced by both the Lagrangian velocity integral time scale and Kolmogorov time scale. Results on the logarithm of the pseudo-dissipation are in support of its modeling as a diffusion process with one-time Gaussian statistics. As the Reynolds number increases, the statistics of dissipation and enstrophy become more similar while their logarithms have significantly longer time scales.