Supplementary material for 'Noise induced effects in the axisymmetric spherical Couette flow'

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 <i>Philosophical Transactions</i> paper (Part 2)'.

本研究针对数值模拟与实验场景下含噪声的轴对称宽间隙球形库埃特流动（spherical Couette flow）展开系统分析。此类研究具备重要学术价值，因自然界中绝大多数流动均受随机涨落影响。通过向内球体旋转施加时间上随机且均值为零的涨落，即可为流动引入噪声。粘性不可压缩流体的流动可通过两种方式驱动：仅依靠内球体旋转，或借助双球体同向旋转共同驱动。研究发现，附加噪声作用下会产生平均流动；在特定条件下，经向动能相对周向分量的相对放大倍数更高这一现象亦被观测到。计算所得的流动速度通过激光多普勒测速仪（laser Doppler anemometer）的测量结果得到了验证。本研究提出了一个理论模型，用以阐释通过改变双球体同向旋转参数所驱动流动的经向动能快速增长机制。针对仅由内球体旋转驱动的流动开展的线性稳定性分析显示，对应首次失稳起始的临界雷诺数（critical Reynolds number）出现了降低。此外，在此工况下，当流动趋近临界雷诺数时，平均流动的生成量会呈现局部极小值，这一结果与现有理论预测相符。本文隶属于“纪念泰勒开创性《哲学汇刊》论文发表百年——泰勒库埃特流动及相关流动（第二部分）”专题刊。