Pattern selection and transition to turbulence in propagating waves

Abstract We present a study of oscillatory convection in two experimental systems: ethanol-water mixtures in a rectangular container heated from below and a thin layer of nematic liquid crystals under low frequency ac voltage. In both systems the first bifurcation is the transition to travelling waves (TW) with finite wave vector and frequency. We report experimental observations of a sequence of spatial structures and dynamical behaviour of nonlinear TW in a regime of a weak nonlinearity. Most of the rich variety of spatial and dynamical behaviour which we observe in one-dimensional finite geometries has been reproduced by numerical simulations based on a simple model of coupled Ginzburg-Landau equations which considers only the combination of translation and finite geometry. More complicated spatio-temporal behaviour of TW in cells with two-dimensional geometry which initiated by defect nucleation is attributed to the mechanism of modulational instability of TW.

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