Chaotic advection in a three-dimensional volume-preserving potential flow

2017-03-03T01:15:45Z (GMT) by Smith, Lachlan Dean
While mixing and particle transport in 2D incompressible flows are well-understood, much less is known about 3D incompressible flows. This is because the addition of a third dimension adds to the topological complexity, and more importantly, the link between 2D incompressible flows and Hamiltonian systems that proved so fruitful breaks down for 3D flows. Therefore, there is a need for fundamental studies on 3D fluid transport and mixing, with applications in groundwater flows, micro-fluidics, industrial mixers and biological flows. Here fluid transport and mixing is studied using a model fluid flow, the 3D Reoriented Potential Mixing (3DRPM) flow, as a case study to reveal novel transport mechanisms and associated coherent structures that are generic to 3D volume-preserving flows. The 3DRPM flow consists of a periodically reoriented dipole flow, and is a 3D analogue of the 2D RPM flow that has been studied in the past. In the 3DRPM flow it is found that there are a number of competing transport mechanisms, that together drive a transition from 1D to 3D particle transport. Periodic points and lines play an important role for all volume-preserving flows, revealing regions of chaos and impenetrable barriers to transport. Here it is shown that degenerate/parabolic periodic points are particularly important, as they represent bifurcations in flow stability. Conversely, discontinuous deformations are an unexpected consequence of dipole reorientation, akin to slip deformations seen in shear-banding materials, and occur even though the steady dipole flow is smooth. This has a significant impact on the transport behaviour of particles, and can either enhance or impede the rate of mixing. The combination of smooth and discontinuous deformations is generic to a wide range of systems, including flows with extraction and reinjection of fluid, granular flows, and deformations of shear-banding materials. Here it is shown that discontinuous deformations can destroy impenetrable barriers to transport, allowing greater freedom for particle transport. In 3D systems they can create a novel mechanism for fully 3D transport that is similar in effect to Resonance Induced Dispersion.