One- and two-particle Lagrangian acceleration correlations in numerically simulated homogeneous turbulence

Lagrangian statistics of the fluid particle acceleration are studied by direct numerical simulation, in stationary isotropic turbulence (at three different Reynolds numbers) and homogeneous shear flow with uniform mean shear rate. The one-particle acceleration autocorrelation decays rapidly with time, with a zero crossing just over two Kolmogorov time scales. In contrast, two-particle correlations are relatively persistent, especially for particle pairs of small initial separation distance. Results for intermediate times at a Taylor-scale Reynolds number of 140 resemble a t−1 inertial-range scaling suggested in the literature, but even higher Reynolds numbers are needed for more definitive comparisons. Use of a theoretical argument and conditional sampling indicates that the two-particle correlation is determined by a coupling between a correlation localized in space and a particle-pair separation probability density of positive skewness. The scenario which emerges is that whereas some fluid particles accelerate rapidly away from each other, the majority of particle pairs can still be relatively close together and hence help maintain the two-particle correlation at significant levels. Acceleration correlations in homogeneous shear flow are found to display a tendency toward local isotropy.