  In the paper we consider the solution of an advection equation with rapidly
changing coefficients $\partial_t
u_\eps+(1/\eps)V(t\eps^{-2},x/{\eps})\cdot\nabla_x u_\eps=0$ for $t<T$ and
$u_\eps(T,x)=u_0(x)$, $x\in\bbR^d$. Here $\eps>0$ is some small parameter and
the drift term $\left(V(t,x)\right)_{(t,x)\in \bbR^{1+d}}$ is assumed to be a
$d$-dimensional, vector valued random field with incompressible spatial
realizations. We prove that when the field is Gaussian, locally stationary,
quasi-periodic in the $x$ variable and strongly mixing in time the solutions
$u_\eps(t,x)$ converge in law, as $\eps\to0$, to $ u_0(x(T;t,x))$, where
$\left(x(s;t,x)\right)_{s\ge t}$ is a diffusion satisfying $x(t;t,x)=x$. The
averages of $u_\eps(T,x)$ converge then to the solution of the corresponding
Kolmogorov backward equation.
