Passive particle transport in three-vortex flow

We study transport of tracer particles in a two-dimensional incompressible inviscid how produced by three point vortices of equal strength. Time depen dence of the flow caused by vortex motion gives rise to chaotic tracer traj ectories, which fill parts of the flow plane referred to as mixing regions. For general vortex positions, a large connected mixing region (chaotic sea ) is formed around vortices. It comprises a number of coherent fluid patche s (islands), which do not mix with the rest of the chaotic sea, inside them particle motion is predominantly regular; three near-circular islands surr ounding vortices are distinguished by their robust nature. Tracers in the c haotic sea rotate around the center of vorticity in an irregular way. Their trajectories are intermittent, long flights of almost regular motion are c aused by trappings in the boundary regions of regular islands. The statisti cs of tracer rotation exhibits anomalous features, such as faster than line ar growth of tracer ensemble variance and asymmetric probability distributi on with long power tails. Exponent of the variance growth power law is diff erent for different time ranges. Central part of the tracer distribution an d its low (noninteger) moments evolve in a self-similar way, characterized by an exponent, which is different from that of the variance, and contrary to the latter is constant in time. Algebraic tails of the tracer distributi on, controlling the behavior of the variance, are responsible for this effe ct. Long correlations in tracer motion lead to non-Poissonian distribution of Poincare recurrences in the mixing region. Analysis of long recurrences proves, that they are caused by tracer trappings inside boundary layers of islands of regular motion, which always exist inside the mixing region. Sta tistics of Poincare recurrences and trapping times exhibit power-law decay, indicating absence of a characteristic relaxation time. Values of the deca y exponent for recurrences and for escape from the analyzed traps are very close to each other; long correlations are not dominated by a single trap, but are a cumulative effect of all of them, relative importance of a trap i s determined by its size, and by its rotation frequency with respect to the background.