  We consider a particle undergoing Brownian motion in Euclidean space of any
dimension, forced by a Gaussian random velocity field that is white in time and
smooth in space. We show that conditional on the velocity field, the quenched
density of the particle after a long time can be approximated pointwise by the
product of a deterministic Gaussian density and a spacetime-stationary random
field $U$. If the velocity field is additionally assumed to be incompressible,
then $U\equiv 1$ almost surely and we obtain a local central limit theorem.
