Takeda Kazuki, Duguet Yohann, Tsukahara Takahiro
Department of Mechanical Engineering, Tokyo University of Science, Chiba 278-8510, Japan.
LIMSI-CNRS, Université Paris-Saclay, F-91400 Orsay, France.
Entropy (Basel). 2020 Sep 4;22(9):988. doi: 10.3390/e22090988.
The onset of turbulence in subcritical shear flows is one of the most puzzling manifestations of critical phenomena in fluid dynamics. The present study focuses on the Couette flow inside an infinitely long annular geometry where the inner rod moves with constant velocity and entrains fluid, by means of direct numerical simulation. Although for a radius ratio close to unity the system is similar to plane Couette flow, a qualitatively novel regime is identified for small radius ratio, featuring no oblique bands. An analysis of finite-size effects is carried out based on an artificial increase of the perimeter. Statistics of the turbulent fraction and of the laminar gap distributions are shown both with and without such confinement effects. For the wider domains, they display a cross-over from exponential to algebraic scaling. The data suggest that the onset of the original regime is consistent with the dynamics of one-dimensional directed percolation at onset, yet with additional frustration due to azimuthal confinement effects.
亚临界剪切流中湍流的起始是流体动力学中临界现象最令人费解的表现之一。本研究通过直接数值模拟，聚焦于无限长环形几何结构内的库埃特流，其中内杆以恒定速度移动并带动流体。尽管对于半径比接近1的情况，该系统类似于平面库埃特流，但对于小半径比，识别出了一种定性上新颖的状态，其特征是没有倾斜带。基于周长的人为增加进行了有限尺寸效应分析。展示了有无这种限制效应时湍流分数和层流间隙分布的统计情况。对于更宽的区域，它们呈现出从指数标度到代数标度的转变。数据表明，原始状态的起始与起始时一维定向渗流的动力学一致，但由于方位限制效应而存在额外的阻碍。
