Accurate Analysis of Turbulence Dynamics using Unstable Periodic Flow

使用不稳定周期流精确分析湍流动力学

• 批准号: 17340118
• 负责人: KIDA Shigeo
• 金额: $ 10.29万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17340118/
• 关键词: Unstable periodic flow; Couette system; Turbulent mixing; Passive vector; 不安定周期運動; 線素; 混合; 高対称流; 回転球; Unstable periodic flow; Couette system; Turbulent mixing; Passive vector; 不安定周期運動; 線素; 混合; 高対称流; 回転球

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

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为其统计属性进行定量描述，我们对COUETTE系统中高级的被动向量进行了不稳定的周期性流（UPF）分析。湍流的不可重复性是使湍流研究变得困难的主要原因之一。相比之下，Kawahara和Kida（2001）发现的UPF（具有积极的Lyapunof数字）永远是完全相同的状态。因此，通过使用UPF，我们可以根据部署时间成比例地计算与所需的流量相关的统计信息。我们在此UPF中分发了许多被动向量，并将其拉伸速率和方向与流量结构进行比较。发现那些从相同位置但以不同方向开始的被动向量将在有限的时间（UPF期间的顺序）对准方向。这表明……在被动矢量的方向场上，可以唯一地定义为UPF的时间和位置的函数。然后，我们检查那些在空间中均匀分布的被动向量将如何随着时间的流逝而重新排列。我们将流场分为许多小立方体，并计算每个立方体中被动向量方向的统计数据。被动向量在大多数立方体中都在一条线中对齐。另一方面，有很多立方体将被动向量的方向对齐在平面中。我们确认此类平面与涡旋矢量平行，并且由于流动中强大的管状涡流而引起的广告引起。在被动矢量为潜水员方向的地方周围，流体混合得到了增强。 COUETTE湍流中的主要组织结构是流向涡流，它在壁界附近产生了弹出和甜区。被动矢量的线性比对在流向涡旋的内部以及射血区域中。另一方面，在流向涡流的外围和扫地区域中观察到平面分布。被动矢量的方向分布与流量结构之间的对应关系取决于接近速度（当前时间和过去的大约UPF周期的一半）。在湍流的特征时期，被动向量失去了记忆。这对于考虑湍流混合和发展湍流模型至关重要。较少的