  We study some finite time transport properties of isotropic Brownian flows.
Under a certain nondegeneracy condition on the potential spectral measure, we
prove that uniform shrinking or expansion of balls under the flow over some
bounded time interval can happen with positive probability. We also provide a
control theorem for isotropic Brownian flows with drift. Finally, we apply the
above results to show that under the nondegeneracy condition the length of a
rectifiable curve evolving in an isotropic Brownian flow with strictly negative
top Lyapunov exponent converges to zero as $t\to \infty$ with positive
probability.
