TRANSIENT CHAOTIC MIXING IN OPEN HYDRODYNAMICAL FLOWS

Abstract

We investigate particle motion and mixing in time-dependent open flows with uniform inflow and outflow velocities. The dynamics is typically chaotic, of the transient type that can be observed on finite time scales only. There exists an underlying chaotic set consisting of an infinity of unstable tracer orbits, restricted to a finite domain of the flow. Transient dynamics is accompanied by persistent fractality. The latter is reflected by tracer patterns and by the singularity distribution of the particles’ time delay function. As an illustrative example, we consider a planar incompressible flow modeling the leapfrogging motion of two vortex rings.