Pattern Formation in Viscous Flows
Pattern Formation in Viscous Flows
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粘性流中的模式形成
DOI：
10.1007/978-3-0348-8709-0
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
R. Meyer
中科院分区：
文献类型：
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作者：
R. Meyer
在某些特殊情况下，如果不获得流体运动的数学表示，而在这种情况下实际上可以观察到不稳定性，从而可以在分析结果和实验结果之间进行详细的比较，那么我们是否能够期望完全理解流体流动的不稳定性，这似乎是值得怀疑的。虽然流体动力学方程相当复杂，但有一些构型允许简单的流动模式作为静止解（例如平行板之间或旋转圆柱之间的流动）。这些流型只能在一定的参数范围内获得。对于不在这些区域中的参数值，它们无法获得，主要是由于两个不同的原因：·解的数学存在性是参数依赖的;或者·解在数学上存在，但它们不稳定。为了找到稳定的稳态，需要两个步骤：必须找到稳态并确定其稳定性。
It seems doubtful whether we can expect to understand fully the instability of fluid flow without obtaining a mathematical representa tion of the motion of a fluid in some particular case in which instability can actually be ob served, so that a detailed comparison can be made between the results of analysis and those of experiment.-Gl Taylor (1923) Though the equations of fluid dynamics are quite complicated, there are configurations which allow simple flow patterns as stationary solutions (eg flows between parallel plates or between rotating cylinders). These flow patterns can be obtained only in certain parameter regimes. For parameter values not in these regimes they cannot be obtained, mainly for two different reasons:• The mathematical existence of the solutions is parameter dependent; or• the solutions exist mathematically, but they are not stable. For finding stable steady states, two steps are required: the steady states have to be found and their stability has to be determined.