Accurate Analysis of Turbulence Dynamics using Unstable Periodic Flow

流体混合是湍流最突出的特征之一。为了了解混合动力学并对其统计特性进行定量描述，我们对Couette系统中的被动矢量进行了不稳定周期性流（UPF）分析。湍流的不可重复性是造成湍流研究困难的主要原因之一。相比之下，Kawahara和Kida（2001）发现的具有正李雅普洛夫数的UPF永远重复相同的状态。因此，通过使用UPF，我们可以按照所投入时间的比例精确地计算与流相关的统计数据。我们在该UPF中分布了许多被动向量，并将它们的拉伸速率和方向与流动结构进行了比较。研究发现，从同一位置出发但方向不同的被动矢量，会在有限时间内（UPF周期的数量级）朝同一方向排列。这表明被动矢量的方向场可以唯一地定义为UPF的时间和位置的函数。然后，我们将研究那些均匀分布在空间中的被动向量如何随着时间的推移而重新排列。我们将流场划分为许多小立方体，并计算每个立方体中被动矢量方向的统计量。在大多数立方体中，被动向量排成一条线。另一方面，有相当多的立方体，其中被动向量的方向在一个平面上对齐。我们证实了这些平面与涡度矢量平行，并且它是由流动中强管状涡引起的平流引起的。在这些被动矢量方向不同的地方，流体混合增强。库埃特湍流的主要组织结构是流向涡，它在壁面边界附近形成喷射区和扫掠区。在向流涡内部和抛射区均发现被动矢量的线性排列。另一方面，在向流涡旋的外围和扫掠区观察到平面分布。被动矢量的方向分布与流动结构之间的这种对应关系取决于近过去（在现在和过去大约半个UPF周期之间）。被动矢量在湍流特征时间内失去记忆。这对于考虑湍流混合和建立湍流模型是至关重要的。少

Fluid mixing is one of the most prominent characteristics of turbulence. In order to understand the mixing dynamics and to develop a quantitative description of its statistical properties we performed the unstable-periodic-flow (UPF) analysis of the passive vectors advected in a Couette system. The unrepeatability of turbulence is one of the main causes which make the turbulence research difficult. In contrast the UPF discovered by Kawahara and Kida (2001), which has positive Lyapunof number, repeats exactly the same state for ever. Therefore, by using the UPF, we can calculate the statistics associated with flows as accurately as desired in proportion to the time devoted. We distribute many passive vectors in this UPF, and compare their stretching rate and orientation with the flow structures. It is found that those passive vectors which start at the same position but with different orientation, will align in direction in a finite time (of order of the period of UPF). This suggests th … More at the directional field of passive vectors may be uniquely defined as a function of the time and position of the UPF. We examine then how are those passive vectors that are distributed uniformly in space will rearrange as the time progresses. We divide the flow field into many small cubes, and calculate the statistics of the direction of passive vectors in each cube. The passive vectors are aligned in a line in most of the cubes. On the other hand, there are quite a few cubes in which the directions of passive vectors are aligned in a plane. We confirmed that such planes are parallel to the vorticity vector and that it is caused by the advection due to strong tubular vortices in the flow. The fluid mixing is enhanced around such places where the direction of passive vectors is diverse. The main organized structure in the Couette turbulence is the streamwise vortex, which creates the ejection and sweep regions near the wall boundary. The linear alignment of passive vectors is found in the interior of the streamwise vortices as well as in the ejection region. The planar distribution, on the other hand, is observed in the periphery of the streamwise vortices and in the sweep region. Such correspondence between the directional distribution of passive vectors and the flow structure depends on the near-past (between the present time and the past about a half of the period of UPF). The passive vectors lose their memory in the characteristic time of the turbulence. This is of essential importance in considering turbulence mixing and in developing turbulence model. Less