  We study diffusion processes and stochastic flows which are time-changed
random perturbations of a deterministic flow on a manifold. Using non-symmetric
Dirichlet forms and their convergence in a sense close to the
Mosco-convergence, we prove that, as the deterministic flow is accelerated, the
diffusion process converges in law to a diffusion defined on a different space.
This averaging principle also holds at the level of the flows. Our
contributions in this article include: a proof of an original averaging
principle for stochastic flows of kernels; the definition and study of a
convergence of sequences of non-symmetric bilinear forms defined on different
spaces; the study of weighted Sobolev spaces on metric graphs or "books".
