| Even though the first theoretical example of chaotic advection was a three-dimensional flow (Hénon, 1966), the number of theoretical studies addressing chaos and mixing in three-dimensional flows is small. One problem is that an experimentally tractable three-dimensional system that allows for detailed experimental and computational investigation had not been available. We begin by examining a three-dimensional construct (the Sphere Flow) which exhibits chaotic particle trajectories. This is used as a test bed for theory and numerics to aid in subsequent design. Then a prototypical, bounded, three-dimensional, moderate Reynolds number flow is presented; this system lends itself to detailed experimental observation and allows for high precision computational inspection of geometrical and dynamical effects. The flow structure, captured by means of cuts with a laser sheet (experimental Poincaré section), is visualized via continuously injected fluorescent dye streams, and reveals detailed chaotic structures and chains of high period islands. Numerical experiments are performed and compared with particle image velocimetry (PIV) and flow visualization results. Predictions of existing theories for chaotic advection in three-dimensional volume preserving flows are tested. The ratio of two frequencies of particle motion—the frequency of motion around the vertical axis and the frequency of recirculation in the plane containing the axis—is identified as the crucial parameter. Using this parameter, the number of islands in the chain can be predicted. The same parameter—using as a base-case the integrable motion—allows the identification of operating conditions where small perturbations lead to nearly complete mixing. |
