沿旋转流体轴线平移的球体绕流：对Maxworthy实验的数值重访
Flow past a sphere translating along the axis of a rotating fluid: Revisiting numerically Maxworthy's experiments
AI总结：
本文数值重访了Maxworthy关于旋转流体中沿轴平移球体绕流的实验，揭示了Taylor柱与惯性波特征，确定了阻力与扭矩标度律，并证实轴向限制效应是导致实验与理论长期差异的根源。
摘要：
我们计算了刚性球体在一个充满低粘度流体并做刚体旋转的大型圆柱容器中沿轴线稳定平移所诱导的流场，该球体被约束以与未受扰动流体相同的速率旋转。模拟覆盖的参数范围与Maxworthy [J. Fluid Mech., vol. 40, pp. 453-479 (1970)] 的实验探索范围相似。我们描述了流场的显著特征，特别是形成于物体前后的Taylor柱的内部特征以及惯性波模式，并确定了作用在球体上的阻力和扭矩。发现在快速和慢速旋转条件下，扭矩变化分别遵循两种截然不同的规律。通过考察球体附近主导轴向涡量分布的平衡关系，预测了相应的标度律。阻力结果与Tanzosh & Stone [J. Fluid Mech., vol. 275, pp. 225-256 (1994)] 针对无惯性机制提出的半经验定律高度吻合。发现该定律甚至适用于惯性效应很大的机制，前提是旋转效应也足够大。轴向限制的影响被证明会显著增加快速旋转配置中的阻力，且容器长度必须大约比球体大一千倍，这种影响才能变得微乎其微。所报告的模拟证实，这种限制效应是Maxworthy结果与理论预测之间长期存在差异的根源。
英文摘要：
We compute the flow induced by the steady translation of a rigid sphere along the axis of a large cylindrical container filled with a low-viscosity fluid set in rigid-body rotation, the sphere being constrained to spin at the same rate as the undisturbed fluid. The parameter range covered by the simulations is similar to that explored experimentally by Maxworthy [\textit{J. Fluid Mech.}, vol. 40, pp. 453-479 (1970)]. We describe the salient features of the flow, especially the internal characteristics of the Taylor columns that form ahead of and behind the body and the inertial wave pattern, and determine the drag and torque acting on the sphere. Torque variations are found to obey two markedly different laws under rapid- and slow-rotation conditions, respectively. The corresponding scaling laws are predicted by examining the dominant balances governing the axial vorticity distribution in the body vicinity. Results for the drag agree well with the semi-empirical law proposed for inertialess regimes by Tanzosh \& Stone [\textit{J. Fluid Mech.}, vol. 275, pp. 225-256 (1994)]. This law is found to apply even in regimes where inertial effects are large, provided rotation effects are also large enough. Influence of axial confinement is shown to increase dramatically the drag in rapidly rotating configurations, and the container length has to be approximately a thousand times larger than the sphere for this influence to become negligibly small. The reported simulations establish that this confinement effect is at the origin of the long-standing discrepancy existing between Maxworthy's results and theoretical predictions.
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