Chaotic advection in pulsed source-sink systems

Pulsed operation of a source and a sink is a classic approach to generating chaotic advection in the unbounded plane. This approach provides motivation for mixing laminar flows in high-aspect-ratio volumes using an arrangement of sources and sinks.~ In bounded systems the sources and sinks must operate in pairs in order to conserve volume.~ When the sources and sinks are arranged on the boundary of a circular domain, particle motions are given explicitly by a discrete mapping. This mapping is used to explore the optimal operating parameters for producing chaos with three different source-sink configurations in a circular domain.