Instabilities of a horizontal shear flow with a free surface
Instabilities of a horizontal shear flow with a free surface
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具有自由表面的水平剪切流的不稳定性
DOI：
10.1017/s0022112098008957
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发表时间：
1998
影响因子：
3.7
通讯作者：
M. Longuet
中科院分区：
文献类型：
--
作者：
M. Longuet
本文推广了Stern&Adam(1973)的简单剪切流模型，其中均匀涡度和深度的一层覆盖在无限深的流体上，增加了一层等厚度等速度的上层流体。这样一来，许多实验观测到的速度分布就可以近似。这种模型的简正模不稳定性可以解析地求出，并通过解一个四次多项式方程来计算它们的性质。色散关系是由弗劳德数和H_1/H_2之比决定的，其中H_1和H_2分别表示表层和剪切层底部的平均深度。结果发现，当H1/H2[GES]为0.4924时，两个在H1/H2中等或较小时截然不同的不稳定性分支可以合并。还计算了增长最快的模式及其波长。该结果被应用于拖曳物体产生的表面流动的一些例子，以及用于稳定的溢流破碎器。
The simple shear-flow model of Stern & Adam (1973), in which a layer of uniform vorticity and depth overlies an infinitely deep fluid, is here extended by the addition of an upper fluid layer of uniform thickness and constant velocity. In this way many experimentally observed velocity profiles can be approximated. The normal mode instabilities of such a model can be found analytically, and their properties calculated through the solution of a quartic polynomial equation. The dispersion relation is here determined and illustrated in its dependence on the Froude number and on the ratio H1/H2, where H1 and H2 denote the mean depths of the surface layer and the base of the shear layer, respectively. It is found that two branches of instability which are distinct when H1/H2 is moderate or small can become merged when H1/H2[ges ]0.4924. Also calculated are the fastest-growing modes, and their wavelengths. The results are applied to some examples of surface flows generated by towed bodies, and to steady spilling breakers.