  Standard and anomalous transport in incompressible flow is investigated using
multiscale techniques. Eddy-diffusivities emerge from the multiscale analysis
through the solution of an auxiliary equation. From the latter it is derived an
upper bound to eddy-diffusivities, valid for both static and time-dependent
flow. The auxiliary problem is solved by a perturbative expansion in powers of
the P\'eclet number resummed by Pad\'e approximants and by a conjugate gradient
method. The results are compared to numerical simulations of tracers dispersion
for three flows having different properties of Lagrangian chaos. It is shown on
a concrete example how the presence of anomalous diffusion can be revealed from
the singular behaviour of the eddy-diffusivity at very small molecular
diffusivities.
