  The motion of weakly inertial Brownian particles, transported by steady
two-dimensional fluid flows, is investigated by means of asymptotic methods. We
focus on the phenomenon of noise-induced separatrix crossing, which can force
particles to enter or exit recirculation cells in an unpredictable manner. An
analytical expression for the probability of separatrix crossing is obtained.
It can be applied to a wide variety of flows, provided some elementary
kinematical quantities of the fluid flow are known. It does not require to
solve particle trajectories.
