Instability of Three‐Layer Viscous Stratified Flow
Instability of Three‐Layer Viscous Stratified Flow
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三层粘性分层流的不稳定性
DOI：
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发表时间：
1969
期刊：
影响因子：
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通讯作者：
Chin‐Hsiu Li
中科院分区：
文献类型：
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作者：
Chin‐Hsiu Li
研究了不同粘度流体的三层叠加在两个水平面之间的平面库埃特流的不稳定性。发现存在两种扰动模式，分别由两个界面主导。发现对于某些深度和粘度比值，流动在波数 α 的零阶近似中不稳定。这是由于当下界面处的自由波迫使上界面处的自由波时出现一种共振。从先前获得的结果可知，单个粘度不连续表面的存在将导致不稳定。附加不连续表面的存在可能稳定也可能不稳定，具体取决于附加界面处的深度和粘度比的值。
Instability of plane Couette flow of three superposed layers of fluids of different viscosity between two horizontal planes is investigated. It is found that there are two modes of disturbance dominated, respectively, by the two interfaces. The flow is found to be unstable in the zero‐order approximation of wavenumber α for certain values of the depth and viscosity ratios. This is owing to a sort of resonance which prevails when a free wave at the lower interface forces a free wave at the upper interface. As is known from results previously obtained, the existence of a single surface of viscosity discontinuity will cause instability. The presence of an additional surface of discontinuity may or may not be stabilizing, depending upon the values of the depth and viscosity ratios at the additional interface.