Topological mixing in viscous fluids
Mixing very viscous fluids seems difficult without the help of turbulence. However, some simple low-Reynolds-number flows can exhibit very complicated Lagrangian trajectories and thus good mixing. This phenomenon is called chaotic advection. It has recently been investigated from a topological perspective in the case of flows generated by moving stirrers. The motion of the stirrers is visualized in a space-time plot and regarded as an entangled braid whose complexity is a measure of mixing. I review this topological theory of mixing and show that it is possible to extend this formalism to periodic orbits of the flow in addition to rods. We call these periodic orbits ''ghost rods'' because they play the same role as stirrers.
This is a weekly series of informal talks given primarily by members of the soft condensed matter and statistical mechanics groups, but is also open to members of other groups and external visitors. The aim of the series is to promote discussion and learning of various topics at a level suitable to the broad background of the group. Everyone is welcome to attend..