Why do Knotted Vortices Stretch?

In this presentation we model the motion of particles in the frozen flow-field of knotted and unknotted vortices.  By observing the time evolution of a seeded dye path we observe a qualitative difference in the stretching behavior based on the topology of the vortex.  Additionally, we compute the Finite-Time Lyapunov Exponent (FTLE) for a plane intersecting the trefoil knot, and find regions of chaotic behavior that correspond to exponential stretching.  These results seem to explain previous experimental observations and numerical simulations, and may have relevance for vortex dominated flows in other contexts, including turbulence.