DYNAMICS OF VORTEX LINES IN THE 3-DIMENSIONAL COMPLEX GINZBURG-LANDAUEQUATION - INSTABILITY, STRETCHING, ENTANGLEMENT, AND HELICES

The dynamics of curved vortex filaments is studied analytically and nu merically in the framework of a three-dimensional complex Ginzburg-Lan dau equation (CGLE). It is shown that a straight vortex line is unstab le with respect to spontaneous stretching and bending in a substantial range of parameters of the COLE, resulting in formation of persistent entangled vortex configurations. The boundary of the three-dimensiona l instability in parameter space is determined. Near the stability bou ndary, the supercritical saturation of the instability is found, resul ting in the formation of stable helicoidal vortices.