In this paper we consider the properties of transient process that always precedes (or completes) the onset (cessation) of the steady fluid flow in a uniformly rotating vertical cylinder. First, we give an elementary (without using the Navier-Stokes equations) and detailed derivation of the equation describing the space and time distribution of angular speeds in the rotating viscous fluid. This expression is used further for the numerical constructing of the dynamic surface profiles. We find that in the case of abrupt stop of cylinder rotation these profiles has an inflection point, while for abrupt start of cylinder rotation such peculiarity is absent. We provide a simple physical explication of this fact. The issues outlined in this article will be useful for undergraduate students, who study the basics of fluid mechanics.

中文翻译：

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匀速旋转或固定垂直圆柱体中非定常旋转流体流动

在本文中，我们考虑了在均匀旋转的垂直圆柱体中始终先于（或完成）稳定流体流动开始（停止）的瞬态过程的特性。首先，我们给出了描述旋转粘性流体中角速度的空间和时间分布的方程的基本（不使用 Navier-Stokes 方程）和详细推导。该表达式进一步用于动态表面轮廓的数值构造。我们发现，在圆柱体旋转突然停止的情况下，这些轮廓具有拐点，而对于圆柱体旋转的突然启动，这种特性不存在。我们对这一事实进行了简单的物理解释。本文中概述的问题将对学习流体力学基础知识的本科生有用。