Applied fluid chaos: designing advection with periodically reoriented flows for micro to geophysical mixing and transport enhancement

Beginning with motivating examples of chaotic fluid advection applied to control mixing and scalar transport in devices, in biophysical flows, and in environmental and geophysical flows, I discuss basic features and organizing ideas of chaotic advection and transport in planar flows. Due to the combination of kinematics and continuity, steady planar flows must mix poorly; the flow designer must add some time-dependence that causes streamlines to cross at successive times (a simple though effective heuristic). Unstable manifolds of hyperbolic points in flows are the "highways" along which transport takes place. These structures emerge from the way the fluid is stirred and change as stirring parameters vary, leading to fractal distributions of transport rates in the control parameter space of flows. This has important implications for designing applications because it means that small variations in parameters can lead to large changes in performance. Optimum designs require knowledge of the complete parametric variation of transport properties for a given flow. As an example, I explore mixing and scalar advection-diffusion transport with the class of periodically reoriented flows, which is often simple to implement for applications, yet imposes, via its symmetries, a rich structure onto chaotic transport that includes generating sub-harmonic resonance "tongues" of the mixing and transport rates in the flows' control parameter space. My objective in this chapter is to impart to the reader the ability to recognize, design, and use chaotic advection to profitably shape and constrain his or her own investigations