Turbulent Pair Diffusion
  Kinematic Simulations of turbulent pair diffusion in planar turbulence with a -5/3 energy spectrum reproduce the results of the laboratory measurements of Jullien Phys. Rev. Lett. 82, 2872 (1999), in particular the stretched exponential form of the PDF 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 times. This dependence is consistent with the topological picture of turbulent pair diffusion 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. 
F.Nicolleau and J. C. Vassilicos