  We study diffusion processes driven by a Brownian motion with regular drift
in a finite dimension setting. The drift has two components on different time
scales, a fast conservative component and a slow dissipative component. Using
the theory of Dirichlet form and Mosco-convergence we obtain simpler proofs,
interpretations and new results of the averaging principle for such processes
when we speed up the conservative component. As a result, one obtains an
effective process with values in the space of connected level sets of the
conserved quantities. The use of Dirichlet forms provides a simple and nice way
to characterize this process and its properties.

Probability