Super diffusion of bedload tracer transport at intermediate time scales explained via a new analytical formulation

Anomalous diffusion of bedload transport is typically inferred from the tail characteristics of step length and/ or waiting time distributions. However, since this approach is valid only for the long term asymptotic transport process, the mechanism of anomalous diffusion observed at intermediate time scales in field and numerical simulations remains unclear. Here we propose a modified active layer formulation by incorporating a slow process of tracer burial from the active layer into the substrate layer underneath, to account for a simplified form of vertical exchange of tracers during the streamwise transport. We demonstrate, by the obtained analytical solutions, that this formulation can capture the key characteristics of the tracer transport in terms of the advective slowdown and super-diffusion observed in field and numerical studies. By the solution for the variance of the tracer population, we find that the burial effect corresponds to an advection-induced scaling term (∝ t³) at the intermediate time scale, explaining the super diffusion as an accelerated streamwise separation between two distinct groups of tracers consisting of travelling and buried (immobile) particles, respectively.