Chaotic advection in oscillatory flows

Bruno Eckhardt and Erwan Hascoet,
Fachbereich Physik, Philipps Universitat Marburg, 35032 Marburg

In a time-periodic but reversible flow trajectories return to their starting points and there can be no chaos.
Experiments on 2-d flows with periodic and reversible driving forces (Gollub et al) do show chaos, and the question
arises where reversibility is lost. We discuss two mechanisms: for small Reynolds number in the linear Stokes regime
reversibility is lost by a viscous dephasing of the different spatial modes that enter the response of the fluid. For
larger Reynolds numbers inertial effects dominate. We also show how reflection symmetries in the driving can prevent
large scale transport.