论文标题
杆的对齐统计数据与Lagrangian伸展方向在通道流动
Alignment statistics of rods with the Lagrangian stretching direction in a channel flow
论文作者
论文摘要
在均质的各向同性湍流中，已知细长的杆与拉格朗日拉伸方向保持一致。但是，对齐程度如何取决于杆的纵横比。此外，实际关注的许多实际流动都是各向异性和不均匀的。在这里，我们研究了杆在通道流中的拉格朗日拉伸方向的对齐，该通道流在中心附近近似均匀且各向同性，但在墙壁附近不均匀和各向异性。我们的主要问题是杆和拉格朗日拉伸方向之间的相对角度分布取决于杆的纵横比以及杆与通道壁的距离。我们发现该分布表现出了两种状态：一个与随机不相关的运动相对应的小角度的高原，以及描述大型偏移的幂律尾巴。相对角的方差通过高原的宽度描述。我们发现，与通道墙附近的河道中心附近的细长杆与拉格朗日拉伸方向更好地对齐。这些观察结果是根据基于Jeffery方程的简单统计模型来解释的，该模型在定性的渠道中心附近，并在通道墙附近进行了定量。最后，我们讨论了结果对附近杆方向之间相对角度分布的后果（Zhao等，Phys。Rev.Fluids，第4卷，2019年，2019年，054602）。
In homogeneous isotropic turbulence, slender rods are known to align with the Lagrangian stretching direction. However, how the degree of alignment depends on the aspect ratio of the rod is not understood. Moreover, many flows of practical interest are anisotropic and inhomogeneous. Here we study the alignment of rods with the Lagrangian stretching direction in a channel flow, which is approximately homogeneous and isotropic near the center but inhomogeneous and anisotropic near the walls. Our main question is how the distribution of relative angles between a rod and the Lagrangian stretching direction depends on the aspect ratio of the rod and upon the distance of the rod from the channel wall. We find that the distribution exhibits two regimes: a plateau at small angles that corresponds to random uncorrelated motion, and power-law tails that describe large excursions. The variance of the relative angle is described by the width of the plateau. We find that slender rods near the channel center align better with the Lagrangian stretching direction, compared to those near the channel wall. These observations are explained in terms of simple statistical models based on Jeffery's equation, qualitatively near the channel center and quantitatively near the channel wall. Lastly we discuss the consequences of our results for the distribution of relative angles between the orientations of nearby rods (Zhao et al., Phys. Rev. Fluids, vol. 4, 2019, 054602).
