Pattern Formation and Turbulence in Electrohydrodynamic Instability

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The stability diagram of the normal roll pattern in electroconvection is nematic liquid crystals in experimentally determined in this study. The stable wave number bands of the normal rolls are determined for the frequency of applied voltage. We find that the mode destabilizing the normal rolls is of the zigzag type for low frequencies of the applied voltage and at higher frequencies mainly of the skewed varicose type. The change of the destabilizing mode of the normal rolls is closely related to the different transition scenarios to weak turbulence. We find at first time its three different routes. With increasing amplitude of the external voltage, at low frequencies the normal-rolls are followed by a zigzag like pattern and at higher frequencies they are followed by a novel vacillating defect-lattice. Both secondary patterns are therefore on a diffrent route to weak turbulence to which they bifurcate finally at higher voltages. This kind of pattern selection can be realized through d … More efect dynamics, such as nucleation and annihilation of defects, for two dimensional case and by phase slip process for one dimensional system. In this study, in order to understand pattern dynamics, the phase slip process for periodic pattern-forming systems in investigated experimentally and theoretically. The general theoretical analysis of the phase slip process are supplimented by a computer simulation for one dimensional Ginzburg-Landau equation and compared with experimental results in the electrohydrodyanmic convection in one dimensional cells. The amount of phase shift during one phase slip process, the evolutions of a characteristic width of a phase slip core and of its amplitude experimentally obtained agree well with both analytical and simulated ones. In electrohydorodynamic convection, on the other hand, turbulence 1-turbulence 2(DSM1-DSM2)transition, which is nontrivial phenomena, is observed when high voltage (typically 4-5 times of onset voltage V_c for convection)is applied. This transition is local, occurs via production of nuclei of new phase and shows dynamic hysteresis which means hysteresis due to the characteristic relaxation time scale of the system. As a frezuency f is increased the width of hysteresis is shrinked and disappears at certain frequency f_c. The transient properties during turbulence 1-turbulence 2 transition are also studied and the temporal development of distribution probability is obtained. while far from transition threshold the distribution shows always single peak, close to the threshold it shows double peaks in the late stage of transient process, i. e. a transient multimodality. This indicates that the instability of T1-T2 transition is due to the symmetry breaking by intrinsic randomness of a system, i. e. DSM1-turbulence. Less