151 Peripheral mixing of passive scalar at small

Mixing of a passive scalar in the peripheral region close to a wall is investigated by means of accurate direct numerical simulations of both a three-dimensional Couette channel flow at low Reynolds numbers and a two-dimensional synthetic flow. In both cases, the resulting phenomenology can be understood in terms of the theory recently developed by Lebedev & Turitsyn (Phys. Rev. E, vol. 69, 2004, 036301). Our results prove the robustness of the identified mechanisms responsible for the persistency of scalar concentration close to the wall with important consequences in completely different fields ranging from microfluidic applications to environmental dispersion modelling. Mixing of passive tracer in a turbulent flow is a fundamental problem of great technological interest which has undergone a significant theoretical progress in the last years (see Shraiman & Siggia 2000; Falkovich, Gawȩdzki & Vergassola 2001). At low diffusivity and small scales the viscous-convective Batchelor regime of mixing arises for a large value of the Schmidt number Sc = ν/κ, where ν is the kinematic viscosity and κ the molecular diffusivity (Batchelor 1959). In this regime the velocity field can be considered smooth because of the exponential decay of the velocity spectrum. An analogous situation is realized if the tracer is advected by a time-dependent chaotic flow, i.e. a spatially smooth flow at all scales. Several theoretical predictions, including the exponential decay in time of passive scalar fluctuations, given by Pierrehumber