Abnormal mixing of passive scalars in chaotic flows.

We study the relaxation of a passive scalar towards the uniform equilibrium distribution in an advection-diffusion problem where the phase space for the pure advection problem is a mixture of chaotic domains and elliptic islands. Since the advection-diffusion problem is linear, the relaxation can be characterized by the eigenvalues and eigenmodes of the evolution operator. Almost degenerate eigenvalues then give rise to deviations from simple exponential decay behavior. We show by example that the corresponding eigenmodes can be supported by islands or weakly connected chaotic domains. These theoretical considerations are related to some experimental observations in two-dimensional flows.