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Pattern Formation and Turbulence in Electrohydrodynamic Instability

电流体动力学不稳定性中的图案形成和湍流

基本信息

批准号：
02452047
负责人：
KAI Shoichi
金额：
$ 4.29万
依托单位：
The Kyushu Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (B)
财政年份：
1990
资助国家：
日本
起止时间：
1990 至 1991
项目状态：
已结题

项目摘要

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

本文用实验方法确定了电对流中正常滚动斑图的稳定性图。确定了正常轧辊在外加电压频率下的稳定波数带。我们发现，对于施加电压的低频，使正常滚动不稳定的模式是锯齿型的，而在高频，主要是倾斜静脉曲张型的。法向滚转失稳模态的变化与不同的弱湍流转捩方案密切相关。我们第一时间发现了它的三条不同的路线。随着外电压幅值的增加，在低频下，正常辊之后是锯齿状图案，在较高的频率下，它们之后是一种新的摇摆缺陷晶格。因此，两种次级模式都处于不同的弱湍流路线上，它们最终在更高的电压下分叉。这种模式选择可以通过d ...更多信息对二维系统，通过缺陷的形核和湮灭过程，对一维系统，通过相滑移过程等影响动力学。在本研究中，为了了解图案动力学，相位滑移周期图案形成系统的过程中进行了实验和理论研究。本文用一维Ginzburg-Landau方程的计算机模拟补充了相滑移过程的一般理论分析，并与一维胞内电流体动力学对流的实验结果进行了比较。在一个相位滑移过程中的相移量，一个相位滑移核心的特征宽度和它的振幅的实验获得的演变与分析和模拟的一致。另一方面，在电流体动力对流中，当施加高电压（典型地为对流的起始电压V_c的4-5倍）时，观察到湍流1-湍流2（DSM 1-DSM 2）转变，这是非平凡现象。这种转变是局部的，通过产生新相的核而发生，并且显示动态滞后，这意味着由于系统的特征弛豫时间尺度而产生的滞后。随着频率f的增加，磁滞回线的宽度减小，在某一频率f_c处消失。研究了湍流1-湍流2转捩过程中的瞬态特性，得到了分布概率随时间的变化规律。在远离过渡阈值处，分布均为单峰，而在接近过渡阈值处，在过渡过程的后期，分布呈现双峰，即在过渡阈值附近，分布呈现双峰。e.短暂的多模态这表明T_1-T_2跃迁的不稳定性是由于系统的内禀随机性引起的对称性破缺所致。e. DSM 1-湍流。少