Physics Letters A 312 (2003) 355–362 www.elsevier.com/locate/pla Enhanced diffusion regimes in bounded chaotic flows S. Cerbelli, A. Adrover, M. Giona ∗ Dipartimento di Ingegneria Chimica, Centro Interuniversitario sui Sistemi Disordinati, e sui Frattali nell’Ingegneria Chimica, Università di Roma “La Sapienza”, via Eudossiana 18, 00184 Roma, Italy Received 24 September 2002; received in revised form 19 March 2003; accepted 26 March 2003 Communicated by A.R. Bishop Abstract 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.  2003 Elsevier Science B.V. All rights reserved. Keywords: Mixing; Chaotic advection; Advection–diffusion equation; Effective diffusivity The advection–diffusion equation (ADE), (1) ∂φ ∂t + v ·∇φ = Dφ, where v is an solenoidal velocity field (i.e., ∇· v = 0), constitutes an important paradigm for a wide vari- ety of physical processes, encompassing homogeniza- tion in liquid mixtures, pollutant dispersion in the atmosphere, spatiotemporal distribution of fastly re- acting species [1], energy transport in flowing me- dia [2], magnetohydrodynamic instability [3], etc. While it is well known that the presence of the convective field v = v(x,t) can significantly reduce the homogenization time, a complete understanding of the basic mechanisms underlying the cooperative * Corresponding author. E-mail address: max@giona.ing.uniroma1.it (M. Giona). action of convection and molecular diffusion for a generic flow has yet to be achieved. Theoretical work on the fundamental aspects of this subject focused on the interaction between convection and diffusion in steady unbounded flows of either cellular (i.e., spatially periodic) [4–6] or random [7,8] type. The hypothesis that the flow domain is unbounded implies that the long-time, long-distance behavior of the solution of Eq. (1) approaches the solution of a pure diffusion equation with constant tensor diffusivity (effective diffusivity) of the type (2) ∂φ ∂t =  i,j a ij ∂ 2 φ ∂x i ∂x j . By enforcing the equivalence between Eq. (1) and the stochastic differential equation d x = v(x)dt + √ 2D dξ , dξ being the infinitesimal increments of a 0375-9601/03/$ – see front matter  2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0375-9601(03)00536-X