Institute of Mechanics, Lomonosov Moscow state University, 119192 Moscow, Russia.
Department of Physics, University of Helsinki, F1-00014 Helsinki, Finland.
Philos Trans A Math Phys Eng Sci. 2023 May;381(2246):20220124. doi: 10.1098/rsta.2022.0124. Epub 2023 Mar 13.
We study the axisymmetric, wide gap, spherical Couette flow in the presence of noise in numerical simulations and experiments. Such studies are important because most of the flows in nature are subjected to random fluctuations. Noise is introduced into the flow by adding fluctuations to the inner sphere rotation which are random in time with zero mean. Flows of a viscous incompressible fluid are induced either by rotation of the inner sphere only or by the co-rotation of the spheres. Mean flow generation was found to occur under the action of additive noise. A higher relative amplification of meridional kinetic energy compared to the azimuthal component was also observed under certain conditions. Calculated flow velocities were validated by laser Doppler anemometer measurements. A model is proposed to elucidate the rapid growth of meridional kinetic energy for flows induced by varying the co-rotation of the spheres. Our linear stability analysis for flows induced by the rotation of the inner sphere revealed a decrease in the critical Reynolds number, corresponding to the onset of the first instability. Also, in this case, a local minimum of the mean flow generation on approaching the critical Reynolds number was observed, which is consistent with the available theoretical predictions. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal paper (Part 2)'.
我们在数值模拟和实验中研究了轴对称、宽间隙、球形 Couette 流动中的噪声。这些研究很重要，因为自然界中的大多数流动都受到随机波动的影响。通过向内球旋转添加随时间随机且均值为零的波动，将噪声引入流动中。粘性不可压缩流体的流动是通过仅旋转内球或两个球的共旋转来产生的。发现在外加噪声的作用下会产生平均流动。在某些条件下，还观察到相对于角向分量，子午动能的相对放大更高。通过激光多普勒风速计测量验证了计算出的流速。提出了一个模型来阐明由于球体的共旋转而引起的流动中子午动能的快速增长。我们对内球旋转引起的流动的线性稳定性分析表明，临界雷诺数减小，对应于第一不稳定的开始。同样，在这种情况下，在接近临界雷诺数时，平均流动的产生也观察到局部最小值，这与现有的理论预测一致。本文是主题为“Taylor-Couette 和相关流动：Taylor 开创性论文发表一百周年纪念（第 2 部分）”的一部分。
