  Mixing describes the process by which solutes evolve from an initial
heterogeneous state to uniformity under the stirring action of a fluid flow.
Fluid stretching forms thin scalar lamellae which coalesce due to molecular
diffusion. Owing to the linearity of the advection-diffusion equation,
coalescence can be envisioned as an aggregation process. Here, we demonstrate
that in smooth two-dimensional chaotic flows, mixing obeys a correlated
aggregation process, where the spatial distribution of the number of lamellae
in aggregates is highly correlated with their elongation and is set by the
fractal properties of the advected material lines. We show that the presence of
correlations makes mixing less efficient than a completely random aggregation
process because lamellae with similar elongations and scalar levels tend to
remain isolated from each other. We show that correlated aggregation is
uniquely determined by a single exponent which quantifies the effective number
of random aggregation events. These findings expand aggregation theories to a
larger class of systems, which have relevance to various fundamental and
applied mixing problems.
