Pattern Formation and Turbulence in Electrohydrodynamic Instability

实验测定了电对流中法向滚动图的稳定性图为向列型液晶。根据外加电压的频率确定了正常轧辊的稳定波数频带。我们发现，在外加电压的低频下，使正常轧辊失稳的模式是Z字形的，而在较高的频率下，主要是歪曲曲张的模式。正常滚流失稳模式的变化与向弱湍流转变的不同情景密切相关。我们首次发现了它的三条不同的路线。随着外加电压幅值的增大，在低频率下，法线滚子之后是锯齿形图案，而在较高频率下，则是一种新的摆动的缺陷晶格。因此，这两种次级模式都处在不同的路径上，最终在较高的电压下分叉成弱湍流。这种模式选择可以通过d…来实现更有效的动力学，如缺陷的形核和湮灭，对于二维情况，以及对于一维系统的相移过程。本研究从实验和理论两个方面研究了周期性图案形成系统的相移过程，以期对图案动力学有所了解。通过对一维Ginzburg-Landau方程的计算机模拟，提供了相移过程的一般理论分析，并与一维胞内电流体动力对流的实验结果进行了比较。实验得到的单相滑移过程中的相移量、相滑铁心的特征宽度及其幅值的演化与理论分析和模拟结果吻合得很好。另一方面，在电流体动力对流中，当施加高电压(通常是对流起始电压Vc的4-5倍)时，观察到湍流1-湍流2(DSM1-DSM2)转变，这是一个不平凡的现象。这种转变是局域的，通过新相核的产生而发生，并表现出动态滞后，这意味着由于系统特有的驰豫时间尺度而产生的滞后。随着频率f的增加，磁滞宽度减小，并在一定的频率f_c下消失。本文还研究了湍流1-湍流2相变过程中的瞬变特性，得到了分布概率随时间的变化规律。在远离跃迁阈值的情况下，分布始终呈现单峰，在接近阈值时，在瞬变过程的后期呈现双峰，即瞬变多峰。这表明，T1-T2相变的不稳定性是由于系统的固有随机性所致的对称性破缺所致，即DSM1湍流。较少

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