Coiling and Supercoiling of Vortex Filaments in Oscillatory Media

We study the behavior of vortex filaments subject to a uniform density of phase twist in oscillatory media described by the complex Ginzburg-Landau equation. The first instability is a supercritical Hopf bifurcation to stable propagating helical vortices. The secondary instability, also a forward Hopf bifurcation, leads to quasiperiodic supercoiled filaments. The structural changes undergone by these dynamical objects are akin to those of twisted elastic rods, in spite of the presence of the ribbon component of the twist, particular to phase singularities.