Two-particle diffusion and fine-scale structures of turbulence

The purpose of this study is to elucidate the relation between a growth of two-particle distance and the fine-scale structures of turbulence by the three-dimensional direct numerical simulation. It is shown that the Lagrangian bursts of particle-pair Occur in the straining stagnation region, where Delta < 0 (here, Delta = (Q/3)(3) + (R/2)(2) with Q and R being the 2nd and 3rd invariance of the velocity gradient tensor). The scaling law of <(Delta l)(2)>similar to tau' (Delta l and tau are the increment of separation distance and the diffusion time, respectively) has been investigated. It is found that the relation gamma = 6/D-s is useful, where D-s is the power exponent of n(s) approximate to CsL-3 (L/eta)(D)(s) (L and eta are the integral length scale and Kolmogorov microscale, respectively; n(s) is the number density of straining stagnation points; C-s is a dimensionless number). It is also shown that the trajectories of particle-pairs in the (Q, R) space are useful to recognize the fine-scale structure bearing the Lagrangian burst of particle-pair.