Memory Function of Turbulent Fluctuations in Soft-mode Turbulence
Memory Function of Turbulent Fluctuations in Soft-mode Turbulence
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软模湍流中湍流脉动的记忆功能
DOI：
10.1103/physreve.87.012505
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发表时间：
2013
影响因子：
2.4
通讯作者：
S. KAI
中科院分区：
文献类型：
--
作者：
T. NARUMI;J. YOSHITANI;M. SUZUKI;Y. HIDAKA;F. NUGROHO;T. NAGAYA;S. KAI
通过实验观察模态弛豫动力学，以阐明软模湍流的统计物理特性，即在垂直排列的向列液晶中观察到的时空混沌。我们发现了一种与违反时间反转不变性相关的双结构动态交叉，相应的时间尺度满足动态尺度定律。为了确定对偶结构的起源，通过投影算子方法定义了由非热波动引起的记忆函数，并使用实验结果以数值方式获得。记忆函数的结果表明，非热波动可分为马尔可夫贡献和非马尔可夫贡献；后者称为湍流波动（TF）。因此，松弛动力学分为三个特征阶段：无摩擦、早期和晚期。如果由 TF 引起的耗散超过了马尔可夫贡献的耗散，则裸摩擦阶段会收缩；前期和后期则配置二元结构。 TF的记忆效应导致早期的时间可逆弛豫，而湍流混合导致的记忆消失导致后期的简单指数弛豫。此外，由 TF 引起的记忆效应被证明源自称为补丁结构的特征空间一致性。
Modal relaxation dynamics has been observed experimentally to clarify statistical-physical properties of soft-mode turbulence, the spatiotemporal chaos observed in homeotropically aligned nematic liquid crystals. We found a dual structure, dynamical crossover associated with violation of time-reversal invariance, the corresponding time scales satisfying a dynamical scaling law. To specify the origin of the dual structure, the memory function due to nonthermal fluctuations has been defined by a projection-operator method and obtained numerically using experimental results. The results of the memory function suggest that the nonthermal fluctuations can be divided into Markov and non-Markov contributions; the latter is called the turbulent fluctuation (TF). Consequently, the relaxation dynamics is separated into three characteristic stages: bare-friction, early, and late stages. If the dissipation due to TFs dominates over that of the Markov contribution, the bare-friction stage contracts; the early and late stages then configure the dual structure. The memory effect due to TFs results in a time-reversible relaxation at the early stage, and the disappearance of the memory by turbulent mixing leads to a simple exponential relaxation at the late stage. Furthermore, the memory effect due to TFs is shown to originate from characteristic spatial coherency called the patch structure.