TWO-PARTICLE DIFFUSION AND FINE-SCALE STRUCTURES OF TURBULENCE

Abstract

The purpose of this study is to elucidate the relation between a growth of twoparticle distance and the fine-scale structures of turbulence by the three-dimensional direct numerical simulation. It is shown that the Lagrangian bursts of particlepair occur in the straining stagnation region, whereΔ < 0 (here,Δ = (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 〈(Δl)²〉~τ γ (Δl and τ are the increment of separation distance and the diffusion time, respectively) has been investigated. It is found that the relation γ = 6/D _s is useful, where D _s is the power exponent of n _s ≈C _s L−³(L/η)^Ds (L and η 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 particlepairs in the (Q,R) space are useful to recognize the fine-scale structure bearing the Lagrangian burst of particle-pair.