Pattern Formation and Turbulence in Electrohydrodynamic Instability

本研究通过实验确定了电对流中向列型液晶的正横纹稳定性图。根据施加电压的频率确定了正常轧辊的稳定波数带。我们发现，使正常轧辊失稳的模态在施加电压的低频时为之字形模态，在较高频率时主要为歪斜曲张模态。正常滚转失稳模态的变化与不同的弱湍流过渡情况密切相关。我们第一次发现它有三条不同的路线。随着外加电压幅值的增加，在低频率下，正常卷绕后出现锯齿状图案，而在高频率下，正常卷绕后出现新的振荡缺陷晶格。因此，这两种次级模式在通往弱湍流的不同路线上，它们最终在更高的电压下分叉。这种模式选择可以通过二维情况下的缺陷成核和湮灭等更有效的动力学来实现，而一维系统则可以通过相滑移过程来实现。在本研究中，为了理解图案动力学，对周期图案形成系统的相滑移过程进行了实验和理论研究。通过对一维金兹堡-朗道方程的计算机模拟，补充了相滑移过程的一般理论分析，并与一维胞内电液动力对流的实验结果进行了比较。实验得到的一次相滑过程的相移量、相滑铁心特征宽度及其幅值的演变与解析和模拟结果吻合较好。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V_c的4-5倍）时，会观察到湍流1-湍流2（DSM1-DSM2）转变，这是一种非平凡现象。这种转变是局部的，通过新相核的产生而发生，并表现出动态迟滞，即由于系统的特征松弛时间尺度而产生的迟滞。随着频率f的增加，迟滞宽度减小，并在一定频率f_c时消失。研究了湍流1-湍流2跃迁过程中的瞬态特性，得到了分布概率的随时间发展规律。在远离过渡阈值处，分布始终呈现单峰，而在接近过渡阈值处，分布呈现双峰，即瞬态多模态。这表明T1-T2跃迁的不稳定性是由于系统的固有随机性（即dsm1 -湍流）造成的对称性破坏。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