The diffusive transport in two-dimensional incompressible turbulent fields is investigated with the aid of high-quality direct numerical simulations. Three classes of turbulence spectra that are able to capture both short and long-range time-space correlations and oscillating features are employed. We report novel scaling laws that depart from the γ = 7/10 paradigm of percolative exponents and are dependent on the features of turbulence. A simple relation between diffusion in the percolative and frozen regimes is found. The importance of discerning between differential and integral characteristic scales is emphasized.

We propose an analytical approximation for the modified Bessel function of the second kind K ν . The approximation is derived from an exponential ansatz imposing global constrains. It yields local and global errors of less than one percent and a speed-up in the computing time of 3 orders in magnitude in comparison with traditional approaches. We demonstrate the validity of our approximation for the task of generating long-range correlated random fields.