Lévy walks for turbulence: A numerical study

We present a numerical study of enhanced diffusion, for which the mean-squared displacement follows asymptotically 〈r²(t)〉 ∼t^γ, γ > 1. We simulate continuous time random walks with waiting-time distributions which couple the spatial and temporal parameters; this gives rise to Lévy-walks. Our results confirm the theoretically predicted long-time behavior and demonstrate its temporal regime of validity. Furthermore, the simulations document the appearance of (parameter-dependent) transitions between regular and enhanced diffusion regimes.