Tracer dynamics in open hydrodynamical flows as chaotic scattering

Abstract

Methods coming from the theory of chaotic scattering are applied to the advection of passive particles in an open hydrodynamical flow. In a region of parameters where a von Kármán vortex street is present with a time periodic velocity field behind a cylinder in a channel, particles can temporarily be trapped in the wake. They exhibit chaotic motion there due to the presence of a nonattracting chaotic set. The experimentally well- known concept of streaklines is interpreted as a structure visualising asymptotically the unstable manifold of the full chaotic set. The evaluation of streaklines can also provide characteristic numbers of this invariant set, e.g. topological entropy, Lyapunov exponent, escape rate. The time delay distributions are also evaluated. We demonstrate these ideas with the aid of both computer simulations of the Navier-Stokes equations and analytical model computations. Properties that could be measured in a laboratory experiment are discussed.