  The transport of scalar quantities passively advected by velocity fields with
a small-scale component can be modeled at meso-scale level by means of an
effective drift and an effective diffusivity, which can be determined by means
of multiple-scale techniques. We show that the presence of a weak large-scale
flow induces interesting effects on the meso-scale scalar transport. In
particular, it gives rise to non-isotropic and non-homogeneous corrections to
the meso-scale drift and diffusivity. We discuss an approximation that allows
us to retain the second-order effects caused by the large-scale flow. This
provides a rather accurate meso-scale modeling for both asymptotic and
pre-asymptotic scalar transport properties. Numerical simulations in model
flows are used to illustrate the importance of such large-scale effects.
