The transition to fully 3D chaos in Wavy Taylor Vortex flow

Taylor Vortex Flow (TVF) has only 2 degrees of freedom and the domain is fully foliated by Kolmogorov-Arnold-Moser (KAM) surfaces. Mixing thus only occurs via diffusion. For increasing Re TVF is replaced by wavy vortex flow (WVF) which has 3 degrees of freedom. WVF has the potential to exhibit chaotic advection which greatly enhances mixing. The rapid transition from TVF to WVF with increasing Reynolds number is known, however details of the transition are unclear. We introduce a new method for divergence-free interpolation of discrete velocity data and demonstrate how it improves the quality of the predicted Lagrangian flow structures. We show that the WVF perturbation primarily affects the inflow vortex boundary and acts to introduce chaos in the “outer” KAM tori. As the perturbation increases,more of the original KAM tori are destroyed, however new families of tori emerge from the chaos. These encircle the original surfaces in a non-simply connected way and occur for perturbations that are far from small. As the perturbation increases, the new KAM tori likewise succumb to a similar process of destruction until the flow is completely chaotic. This behaviour is essentially the same as exhibited by 2D unsteady incompressible flows. It implies that the 3D steady WVF flow can in a dynamic sense be seen as a composition of Hamiltonian systems that each correspond to a family of KAM tori and its local environment. This is consistent with the fact that 3D steady flows admit (local) expression as a Hamiltonian system in regions anywhere outside isolated stagnation points.