Enhanced diffusion regimes in bounded chaotic flows

We analyze the exponent characterizing the decay towards the equilibrium distribution of a generic diffusing scalar advected by a nonlinear flow on the two-torus. When the kinematics of the stirring field is predominantly regular (e.g., autonomous flows or protocols possessing large quasiperiodic islands) a purely diffusive scaling of the dominant exponent Λ as a function of the diffusivity D, Λ(D)∼D, coexists with a convection-enhanced diffusion regime, with an apparent exponent λ that scales as D. For globally chaotic conditions we find Λ(D)→const as D→0. We provide physical arguments to explain this new phenomenology characterizing chaotic flows