epl draft Localized states in sheared electroconvection

Electroconvection in a thin, sheared fluid film displays a rich sequence of bifurcations between different flow states as the driving voltage is increased. We present a numerical study of an annular film in which a radial potential difference acts on induced surface charges to drive convection. The film is also sheared by independently rotating the inner edge of the annulus. This simulation models laboratory experiments on electroconvection in sheared smectic liquid crystal films. The applied shear competes with the electrical forces, resulting in oscillatory and strongly subcritical bifurcations between localized vortex states close to onset. At higher forcing, the flow becomes chaotic via a Ruelle-Takens-Newhouse scenario. The simulation allows flow visualization not available in the physical experiments, and sheds light on previously observed transitions in the current-voltage characteristics of electroconvecting smectic films. Driven, dissipative nonlinear systems sometimes exhibit spatially localized structures which are analogous to solitons [1]. Examples are found in systems as diverse as vegetation patterns [2], vibrated granular media [3] and ferrofluids [4]. Such states can also arise in fluid-mechanical settings such as binary fluid convection [5, 6] (where they have been called “convectons” [7]), in electroconvecting nematic liquid crystals [8], and in very general model equations [9, 10]. In this Letter, we describe a new and unexpected type of localized patterns: solitary vortex states in two-dimensional, sheared electroconvection. We show numerically that these states can be extremely localized, consisting of only a single, isolated vortex surrounded by a uniform background state. The presence of localized states in this system is surprizing and interesting because it results from the interaction of a circular Couette shear with two-dimensional convection in an especially simple, highly symmetric geometry. Theses states can be experimentally realized using thin free-standing films of smectic liquid crystals [11–16]. Here, direct numerical simulation allows us to study the spatial structure of the full velocity, charge and potential fields [16]. This approach compliments existing theory [12, 16] and experiments [11–15] on this system, which mainly consisted in observations of the total current through the thin film, without flow visualization. The simulation reveals localized states in the form of vortices which travel in the direction of the applied shear. These are preceded by lower-amplitude, extended traveling and oscillatory vortex states. At sufficiently high levels of electrical forcing, the flow becomes chaotic via a Ruelle-Takens-Newhouse scenario [17]. Our results serve to strongly motivate new experiments and theory to elucidate the dynamics of sheared 2D convection. More generally, this system with naturally periodic boundary conditions, and for which forcing and shear are independently controllable, will be an interesting place to examine recent ideas on higher dimensional invariant manifolds on the way to turbulence [18,19]. Our numerical study simulates a laboratory experiment shown schematically in Fig. 1. The system consists of a submicron-thick liquid crystal film freely suspended between concentric circular electrodes. The weakly conducting film is driven to convect when a sufficiently large electric potential is imposed across it. The inner edge of the annular film is held at absolute potential V with respect to infinity, while the outer edge is held at zero potential. In addition to the control parameter associated with this electrical driving force, it is possible to independently rotate the inner electrode, which imposes an azimuthal Couette shear on the film. The experimental signature of convection consists of measurements of the total current through the film, which is increased by convective flow. The film develops a surface charge configuration which is unstable to the applied voltage. This instability is