Research papersBed load transport for a mixture of particle sizes: Downstream sorting rather than anomalous diffusion

- Ballistic rather than anomalous diffusion regimes always emerge for mixtures.
- Mixtures do not satisfy identical and independent distribution (i.i.d.) assumptions.
- Violence of the i.i.d. for mixture deduce ballistic diffusion.
- Ballistic regime matches the deterministic downstream sorting process for mixtures.
- Decreasing number of tracked particles would result in lower diffusion exponent.

The stochastic nature of bed load transport induces diffusion of sediment tracers, which is governed by the dynamics of their bulk behavior over time. By deploying both numerical simulations and flume experiments, the emergent particle diffusion regimes for both uniform and mixed tracer particles were studied and compared. For uniform particles, power-law-distributed resting times Tr produced super-, sub- or normal diffusion regimes for certain values of the tail exponent ν. Based on the assumption that heterogeneity in particle size leads to a power-law distribution of Tr, a completely different diffusion regime emerges in mixtures compared with those obtained from uniform particles with the same value of the tail exponent ν. Mixtures exhibited the same ballistic regime (the variance of travel distance grows as time squared) for different values of ν, and ballistic regimes for mixtures also emerged from several other tested models. Furthermore, our experimental results confirmed the ballistic regime; however, the decreasing number of tracked particles may result in apparent but deceptive sub-diffusion. We conclude that ballistic regimes for mixtures result from violations of the independent and identically distributed (i.i.d.) assumptions, attributing to downstream sorting processes.