Hydrodynamic transitions to chaos in the convection of an anisotropic fluid

We present the first spontaneous sequence of hydrodynamic instabilities due to the evolution of the convective flow from the rest state toward chaos in an anisotropic fluid : a nematic liquid crystal subjected to an AC electric field. The resulting structures are of decreasing symmetry as the control parameter is gradually increased. The study of the streamlines allows the interpretation of the entire sequence by the evolution of the convective flow up to the onset of chaos. We show that the first important step in the flow evolution is the build up of a second mode of rotation which is associated with a pinching instability of the vortex lines. A simple picture is then proposed in order to describe the essential steps of a possible route to chaos, and which could be extended to other convective systems.