Relative diffusion of a pair of fluid particles in the inertial subrange of turbulence

Turbulent diffusion of a pair of fluid particles in 3-dimensional homogeneous and isotropic turbulence was studied using a high-resolution direct numerical simulation (DNS) with 1024(3) grid points. The DNS showed that the mean square of the distance deltax between the two fluid particles grows with time t as <\deltax\(2)>similar toCepsilont(3) in the inertial subrange, which is in agreement with Richardson (1926) and Obukhov (1941), where Capproximate to0.7 and epsilon is the mean dissipation rate per unit mass. A simple Lagrangian closure approximation for <\deltax\(2)> is shown to be in good agreement with the DNS. (C) 2002 American Institute of Physics.