The threefold classification of unstable disturbances in flexible surfaces bounding inviscid flows
The threefold classification of unstable disturbances in flexible surfaces bounding inviscid flows
复制标题
边界无粘流的柔性表面不稳定扰动的三重分类
DOI：
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发表时间：
1963
影响因子：
3.7
通讯作者：
By T. Brooke
中科院分区：
文献类型：
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作者：
By T. Brooke
本文讨论了一般的想法，在系统中，一个灵活的固体与流动的流体耦合的三种不同类型的不稳定性是可能的。这些不稳定性最初由布鲁克本杰明（1960）命名为“A类”、“B类”和“开尔文-亥姆霍兹”不稳定性，它们的集体意义最近由Landahl（1962）阐明。A类和B类扰动本质上是涉及流体和固体之间的保守能量交换的振荡，但它们的稳定性由不可逆过程的净效应决定，所述不可逆过程包括由非保守流体动力向固体的耗散和能量传递。固体中的耗散倾向于稳定B类分布，而不稳定A类分布。C类不稳定性（即“开尔文-亥姆霍兹”型）发生在保守的流体动力导致能量单向转移到固体时。在§ 2中，基本上是通过广义坐标的拉格朗日方法来检验这一思想的，在§ 3中，考虑了流过柔性平面边界的无粘流体的例子。这个例子的处理放大了Landahl的工作，特别是通过包括Miles在他关于风产生水波的系列论文中研究的那种非保守力的影响。
This paper discusses the general idea that in systems where a flexible solid is coupled with a flowing fluid three different types of instability are possible. These were originally designated by Brooke Benjamin (1960) as ‘class A’, ‘class B’ and ‘Kelvin-Helmholtz’ instability, and their collective significance has been clarified recently by Landahl (1962). Class A and class B disturbances are essentially oscillations involving conservative energy-exchanges between the fluid and solid, but their stability is determined by the net effect of irreversible processes, which include dissipation and energy-transfer to the solid by non-conservative hydrodynamic forces. Dissipation in the solid tends to stabilize class B distrbances but to destabilize class A ones. Class C instability (i.e. the ‘Kelvin-Helmholtz’ type) occurs when conservative hydrodynamic forces cause a unidirectional transfer of energy to the solid. In § 2 this idea is examined fundamentally by way of the Lagrangian method of generalized co-ordinates, and in § 3 the example of inviscid-fluid flow past a flexible plane boundary is considered. The treatment of this example amplifies the work of Landahl, in particular by including the effect of non-conservative forces of the kind investigated by Miles in his series of papers on water-wave generation by wind.