Why are Knotted Vortices Unstable?

Concentrated filaments of vorticity are a ubiquitous feature of flow at high Reynolds number.  While many models of vortex behavior focus on simple geometries like rings or lines, vortices in real flows (e.g. turbulence) have a complex structure of links and tangles.  This should significantly affect their behavior: simulations and experiments have shown that even elementary knotted vortices are unstable, unlike rings or lines.  Crucially, this instability appears to be independent of the small scale details of the fluid, and the same general behavior is seen in classical fluid experiments, superfluid simulations, and even reduced order vortex filament models.  This suggests the instability is driven by the large-scale advection of the vortex lines.  In particular, I will show that self-stretching produced by the knotted vortices leads directly to instability and reconnections.