  It is well known that on long time scales the behaviour of tracer particles
diffusing in a cellular flow is effectively that of a Brownian motion. This
paper studies the behaviour on "intermediate" time scales before diffusion sets
in. Various heuristics suggest that an anomalous diffusive behaviour should be
observed. We prove that the variance on intermediate time scales grows like
$O(\sqrt{t})$. Hence, on these time scales the effective behaviour can not be
purely diffusive, and is consistent with an anomalous diffusive behaviour.
