Turbulent pair diffusion

Kinematic simulations of turbulent pair diffusion in planar turbulence with a k(-5/3) energy spectrum reproduce the laboratory results of Jullien et al. [Phys. Rev. Lett. 82, 2872 (1999)]], in particular the stretched exponential form of the probability density function of pair separations and their correlation functions. The root mean square separation is found to be strongly dependent on initial conditions for very long stretches of time. This dependence is consistent with the topological picture where pairs initially close enough travel together for long stretches of time and separate violently when they meet straining regions around hyperbolic points. A new argument based on the divergence of accelerations is given to support this picture.