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We elucidate the impact of diffusive motion on the nature of anomalous dispersion in layered and fibrous disordered media. We consider two types of disorder characterized by quenched random velocities and quenched random retardation properties. Purely advective particle motion is ballistic in both disorder models. This changes dramatically in the presence of transverse diffusion, which leads to dimension-dependent disorder sampling. For d≤3 dimensions, heavy-tailed velocity distributions render large-scale particle motion a correlated Lévy flight, while transport in the quenched random retardation model behaves as a biased continuous time random walk with correlated time increments.

Impact of diffusive motion on anomalous dispersion in structured disordered media: From correlated Lévy flights to continuous time random walks