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Bedload particles in the armoring layer may experience a multi-scale effect and multiple mass transfer rates between mobile and immobile domains. Anomalous transport behaviors and retarded space evolution plume cannot be described by the normal diffusion equation. In this paper, we apply the continuous time random walk model with different distributions of waiting times to capture bedload transport behavior under different conditions. Experimental data indicate that fluctuations of diffusive rates for bedload transport can be captured by the truncated power law (TPL). The retarded plume evolution can be well characterized by an exponential distribution of waiting times and advection-diffusion equation with a retarded kernel. The heavy-tailed snapshots of bedload transport are interpreted in terms of mobile and immobile states.

An investigation on continuous time random walk model for bedload transport