Yan Bowen, Wang Yiqian, Liu Chaoqun
Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China.
School of Mathematical Science, Soochow University, Suzhou 215006, China.
Entropy (Basel). 2022 Dec 23;25(1):25. doi: 10.3390/e25010025.
The Liutex vector is new quantity introduced to represent the rigid-body rotation part of fluid motion and thus to define and identify vortices in various flows. In this work, the intermittency and power-law similarity of the Liutex vector in homogeneous, isotropic turbulence and a turbulent channel are explored. First, we found that the Liutex vector is more intermittent than the vorticity vector in the considered turbulent flows, which indicates that an iso-surface of a Liutex magnitude with an appropriate threshold could capture the major rotating motions or vortical motions of the flow. Second, the three-dimensional energy spectrums of velocity, vorticity (enstrophy spectrum) and the Liutex vector in homogeneous isotropic turbulence are shown to exhibit power laws of -5/3, 1/3 and 1/3 in the inertial subrange, respectively, whilst the Liutex energy spectrum particularly satisfies an additional -10/3 power law in the viscous subrange. This viscous similarity of the Liutex vector is the only power law that survived from the wall presence and is argued to originate from the fact that the Liutex vector represents the rigid part of fluid motion and is free from any shear contamination. The existence of such a viscous similarity law indicates a certain coherence of the small scales of turbulence and could possibly help understand and model turbulence.
Liutex矢量是为表示流体运动的刚体旋转部分而引入的新物理量，从而用于定义和识别各种流动中的涡旋。在这项工作中，我们研究了均匀各向同性湍流和湍流通道中Liutex矢量的间歇性和幂律相似性。首先，我们发现在所考虑的湍流中，Liutex矢量比涡量矢量更具间歇性，这表明具有适当阈值的Liutex模等值面可以捕捉流动的主要旋转运动或涡旋运动。其次，均匀各向同性湍流中速度、涡量（涡量能谱）和Liutex矢量的三维能量谱在惯性子区间分别呈现出-5/3、1/3和1/3的幂律，而Liutex能量谱在粘性子区间特别满足额外的-10/3幂律。Liutex矢量的这种粘性相似性是壁面存在影响下唯一留存的幂律，并且据认为源于Liutex矢量表示流体运动的刚体部分且不受任何剪切污染这一事实。这种粘性相似律的存在表明湍流小尺度具有一定的相干性，并且可能有助于理解和模拟湍流。
