  We study the dynamics of the Taylor-Couette flow of shear banding wormlike
micelles. We focus on the high shear rate branch of the flow curve and show
that for sufficiently high Weissenberg numbers, this branch becomes unstable.
This instability is strongly sub-critical and is associated with a shear stress
jump. We find that this increase of the flow resistance is related to the
nucleation of turbulence. The flow pattern shows similarities with the elastic
turbulence, so far only observed for polymer solutions. The unstable character
of this branch led us to propose a scenario that could account for the recent
observations of Taylor-like vortices during the shear banding flow of wormlike
micelles.
