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

Abstract

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 10243 grid points. The DNS showed that the mean square of the distance δx between the two fluid particles grows with time t as 〈|δx|2〉∼Cεt3 in the inertial subrange, which is in agreement with Richardson (1926) and Obukhov (1941), where C≈0.7 and ε is the mean dissipation rate per unit mass. A simple Lagrangian closure approximation for 〈|δx|2〉 is shown to be in good agreement with the DNS.