Turbulent diffusion in the photosphere as derived from photospheric bright point motion

On the basis of observations of solar granulation obtained with the New Solar Telescope of Big Bear Solar Observatory, we explored proper motion of bright points (BPs) in a quiet-sun area, a coronal hole, and an active region plage. We automatically detected and traced BPs and derived their mean-squared displacements as a function of time (starting from the appearance of each BP) for all available time intervals. In all three magnetic environments, we found the presence of a super-diffusion regime, which is the most pronounced inside the time interval of 10-300s. Super-diffusion, measured via the spectral index, γ, which is the slope of the mean-squared displacement spectrum, increases from the plage area (γ = 1.48) to the quiet-sun area (γ = 1.53) to the coronal hole (γ = 1.67). We also found that the coefficient of turbulent diffusion changes in direct proportion to both temporal and spatial scales. For the minimum spatial scale (22km) and minimum time scale (10s), it is 22 and 19km²s^-1 for the coronal hole and the quiet-sun area, respectively, whereas for the plage area it is about 12km ²s^-1 for the minimum time scale of 15s. We applied our BP tracking code to three-dimensional MHD model data of solar convection and found the super-diffusion with γ = 1.45. An expression for the turbulent diffusion coefficient as a function of scales and γ is obtained.