Richardson's pair diffusion and the stagnation point structure of turbulence

DNS and laboratory experiments show that the spatial distribution of straining stagnation points in homogeneous isotropic 3D turbulence has a fractal structure with dimension D(s)=2. In kinematic simulations the exponent gamma in Richardson's law and the fractal dimension D(s) are related by gamma=6/D(s). The Richardson constant is found to be an increasing function of the number density of straining stagnation points in agreement with pair diffusion occurring in bursts when pairs meet such points in the flow.