Persistence of incomplete mixing: a key to anomalous transport.

Anomalous dispersion in heterogeneous environments describes the anomalous growth of the macroscopic characteristic sizes of scalar fields. Here we show that this phenomenon is closely related to the persistence of local scale incomplete mixing. We introduce the mixing scale ε as the length for which the scalar distribution is locally uniform. We quantify its temporal evolution due to the competition of shear action and diffusion and compare it to the evolution of the global dispersion scale σ. In highly heterogeneous flow fields, for which the temporal evolution of σ is superdiffusive, we find that ε evolves subdiffusively. The anomalous evolutions of the dispersion and mixing scales are complementary, εσ ∝ t. This result relates anomalous global dispersion to the dynamics of local mixing.