On the unsteady rotating fluid flow in a uniformly rotating or fixed vertical cylinder

In this paper we consider the properties of the transient process that always precedes (or completes) the onset (cessation) of 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 a rotating viscous fluid. This expression is used further for the numerical construction of the dynamic surface profiles. We find that in the case of an abrupt stop of cylinder rotation, these profiles have an inflection point, while for an abrupt start of cylinder rotation such a peculiarity is absent. We provide a simple physical explication of this fact. The issues outlined in this article will be useful for undergraduate students studying the basics of fluid mechanics.