Topological Chaos And Mixing in a Three-Dimensional Channel Flow

Passive mixing is investigated in a mathematical model of steady, three-dimensional, laminar flow through a rectangular channel. Efficient stirring is achieved by imposing spatially periodic transverse boundary velocities that generate asymmetric, counter-rotating rolls aligned with the channel axis. The flow is designed and analyzed using the concept of topological chaos, in which complexity is embedded in the flow through the motion of periodic orbits. A lid-driven flow producing topological chaos is found to stir better than a related flow with solid inserts considered previously [M. D. Finn, S. M. Cox, and H. M. Byrne, Phys. Fluids 15, L77 (2003)]. The results demonstrate that topological chaos and the Thurston-Nielsen classification theorem can provide insight into mixing enhancement in steady, three-dimensional flows.