Stability of Spiral Wave Vortex Filaments with Phase Twists

In this paper we investigate the stability of a straight vortex filament with phase twist described by the three-dimensional complex Ginzburg-Landau equation (CGLE). The results of the linear stability analysis show that the straight filament is stable in a limited region of the two parameter space of the CGLE. The stable region is dependent on the phase twist imposed on the filament and shrinks in size as the phase twist is increased. It is also shown numerically that the nonlinear evolution of an unstable initial straight filament can lead to a helical filament.