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

Abstract

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.

Acknowledgements

We gratefully acknowledge support from the National Science Foundation, via Grant CTS-0328314 (PKY) and CTS-0328329 (SBP), and via advanced resources at Pittsburgh Supercomputing Center (PSC) and San Diego Supercomputer Center (SDSC). The 2048³ simulation reported in this work was conducted on the PSC's 3000-processor Compaq Alpha Cluster, with extraordinarily dedicated assistance from our strategic consultant, David O'Neal. At Georgia Tech, Diego Donzis and Elizabeth Kurth also contributed to the conduct of these simulations. Finally, PKY wishes to thank Professor K.R. Sreenivasan of ICTP, Italy for facilitating his participation at the Challenging Turbulent Lagrangian Dynamics Workshop, Roma, Italy (September 2005).