University of Bremen, Center of Applied Space Technology and Microgravity (ZARM), 28359 Bremen, Germany.
Department of Physics, Willamette University, Salem,OR 97301, USA.
Philos Trans A Math Phys Eng Sci. 2023 May;381(2246):20220114. doi: 10.1098/rsta.2022.0114. Epub 2023 Mar 13.
Fluid flows between rotating concentric cylinders exhibit two distinct routes to turbulence. In flows dominated by inner-cylinder rotation, a sequence of linear instabilities leads to temporally chaotic dynamics as the rotation speed is increased. The resulting flow patterns occupy the whole system and sequentially lose spatial symmetry and coherence in the transition process. In flows dominated by outer-cylinder rotation, the transition is abrupt and leads directly to turbulent flow regions that compete with laminar ones. We here review the main features of these two routes to turbulence. Bifurcation theory rationalizes the origin of temporal chaos in both cases. However, the catastrophic transition of flows dominated by outer-cylinder rotation can only be understood by accounting for the spatial proliferation of turbulent regions with a statistical approach. We stress the role of the rotation number (the ratio of Coriolis to inertial forces) and show that it determines the lower border for the existence of intermittent laminar-turbulent patterns. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal paper (Part 2)'.
在旋转同心圆柱之间的流动中，存在两种明显的通向湍流的途径。在以内筒旋转为主导的流动中，随着旋转速度的增加，一系列线性不稳定性导致了暂时混沌的动力学。由此产生的流动模式占据了整个系统，并在过渡过程中依次失去空间对称性和相干性。在外筒旋转为主导的流动中，过渡是突然的，直接导致与层流竞争的湍流区域。我们在这里回顾了这两种通向湍流的主要特征。分岔理论合理地解释了这两种情况下时间混沌的起源。然而，在外筒旋转为主导的流动中灾难性的转变只能通过用统计方法解释湍流区域的空间增殖来理解。我们强调了旋转数（科里奥利力与惯性力的比值）的作用，并表明它决定了间歇性层流-湍流模式存在的下限。本文是主题为“泰勒-库埃特流动及相关流动：泰勒开创性论文百年纪念（第 2 部分）”的一部分。
