Inertial instability of flows on the inside or outside of a rotating horizontal cylinder
Inertial instability of flows on the inside or outside of a rotating horizontal cylinder
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DOI：
10.1017/jfm.2013.530
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发表时间：
2013-11
影响因子：
3.7
通讯作者：
E. Benilov;V. Lapin
中科院分区：
文献类型：
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作者：
E. Benilov;V. Lapin
摘要我们考虑了绕水平轴旋转的圆柱体内部（边缘流）或外部（涂层流）的液体薄膜。如果液体的净体积很小，这种膜已知会朝着具有光滑表面的稳定状态发展，而对于较大的量，流动会产生类似于潮汐的“冲击”。在这项工作中，光滑的薄膜是不稳定的。由于最强的不稳定性发生在与薄膜厚度相当的波长处，因此我们的分析是基于完整的Navier-Stokes方程，而不是基于润滑近似（传统上用于此问题）。它还表明，对于足够小的半径的圆柱体，不稳定性可以抑制表面张力。
Abstract We consider thin liquid films on the inside (rimming flows) or outside (coating flows) of a cylinder with horizontal axis, rotating about this axis. If the liquid’s net volume is small, such films are known to evolve towards a steady state with a smooth surface, whereas, for larger amounts, the flow develops a ‘shock’ similar to a tidal bore. In this work, smooth films are shown to be unstable. Since the strongest instability occurs at wavelengths comparable to the film’s thickness, our analysis is based on the full Navier–Stokes equations, not on the lubrication approximation (which has been traditionally used in this problem). It is also shown that, for cylinders of sufficiently small radii, the instability can be suppressed by surface tension.