  We develop a technique of multiple scale asymptotic expansions along mean
flows and a corresponding notion of weak multiple scale convergence. These are
applied to homogenize convection dominated parabolic equations with rapidly
oscillating, locally periodic coefficients and $\mathcal{O}(\eps^{-1})$ mean
convection term. Crucial to our analysis is the introduction of a fast time
variable, $\tau=\frac{t}{\eps}$, not apparent in the heterogeneous problem. The
effective diffusion coefficient is expressed in terms of the average of
Eulerian cell solutions along the orbits of the mean flow in the fast time
variable. To make this notion rigorous, we use the theory of ergodic algebras
with mean value.
