  Explicit examples of scalar enhanced diffusion due to resonances between
different transport mechanisms are presented. Their signature is provided by
the sharp and narrow peaks observed in the effective diffusivity coefficients
and, in the absence of molecular diffusion, by anomalous transport. For the
time-dependent flow considered here, resonances arise between their
oscillations in time and either molecular diffusion or a mean flow. The
effective diffusivities are calculated using multiscale techniques.
