In this paper, we consider a small ball placed in a liquid-filled transparent cylinder sealed at both ends. When the tube is inclined and spun about the vertical axis like a centrifuge, a heavy ball (more dense than the liquid) will accelerate to either the top or bottom end of the tube depending on its release position while a light ball (less dense than the liquid) will instead tend towards an equilibrium position in the tube. Experimental measurements of the ball’s motion show large disagreements with Stokes’ theory of drag force on the ball. The formation of a rotating column of liquid induced by the Coriolis force, known as a Taylor column, significantly increases the drag on the ball. In this paper, we aim to investigate the equilibrium position as well as the motion path of the ball, with a numerical solution to the 3D time-dependent Navier–Stokes equation in the rotating frame of the tube, as a function of the inclination angle and angular velocity of rotation of the tub...

中文翻译：

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非惯性框架中的分析：旋转管中的球和泰勒柱

在本文中，我们考虑将一个小球放在两端密封的充满液体的透明圆柱体内。当试管倾斜并像离心机一样绕垂直轴旋转时，一个重的球（比液体更稠）将根据其释放位置加速到试管的顶端或底端，而一个轻的球（比液体的密度小）液体）将趋向于在管中达到平衡位置。球运动的实验测量结果显示出与斯托克斯对球的拖曳力理论有很大的分歧。由科里奥利力引起的液体旋转柱（称为泰勒柱）的形成显着增加了球的阻力。在本文中，我们旨在研究球的平衡位置以及运动路径，