Anomalous diffusion in the Kuramoto-Sivashinsky equation

We study the motion of advected particles in the Kuramoto-Sivashinsky equation. We give numerical evidence as well as analytical arguments for anomalous diffusion in which the particle displacement {Δ}r satisfies 〈[{Δ}r(t)]²〉{~}t^η where {η}>1. We show that if the flow is initially seeded with many particles, they will coalesce in time and that a passive scalar density tends to an asymptotic (time dependent) distribution, which, for given initial conditions on the velocity field, is independent of the initial distribution of the passive scalar.