Direct numerical simulation of two-particle relative diffusion in isotropic turbulence

The relative diffusion of fluid particle pairs in statistically stationary isotropic turbulence is studied by direct numerical simulation, at a Taylor-scale Reynolds number of about 90. The growth of two-particle separation exhibits asymptotic stages at small and large diffusion times. Through the two-particle separation, particle-pair velocity correlations are closely related to the Eulerian spatial structure of the turbulence. At large times, the square of the separation distance has a chi-square probability distribution. At the moderate Reynolds number of the simulations, for this asymptotic distribution to be reached before the particles begin to move independently of each other, the initial separation must be small compared to the Kolmogorov scale. In an inertial frame moving with the initial particle velocities, the velocity increments of two fluid particles become uncorrelated only if their initial velocities are uncorrelated, which requires their initial separation be large compared to the integral length scale. For sufficiently large initial separations, the relative velocity increments and mean-square dispersion in this moving frame display a resemblance to inertial range scaling, but with a proportionality constant that is much smaller than classical estimates. At large times, the degree of preferential alignment between the separation and relative velocity vectors is weak, but the product of the separation distance and the velocity component projected along the separation vector is sustained on average.