  We study transport properties of isotropic Brownian flows. Under a transience
condition for the two-point motion, we show asymptotic normality of the image
of a finite measure under the flow and -- under slightly stronger assumptions
-- asymptotic normality of the distribution of the volume of the image of a set
under the flow. Finally, we show that for a class of isotropic flows, the
volume of the image of a nonempty open set (which is a martingale) converges to
a random variable which is almost surely strictly positive.
