Resonant interactions between two trains of gravity waves
Resonant interactions between two trains of gravity waves
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DOI：
10.1017/s0022112062000233
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发表时间：
1962-03
影响因子：
3.7
通讯作者：
M. Longuet-Higgins
中科院分区：
文献类型：
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作者：
M. Longuet-Higgins
在之前的一篇论文中，Phillips（1960）表明，两列或三列重力波可以相互作用，从而产生第四波（第三波），其波数不同于三个主波数k1、k2、k3中的任何一个，其振幅随时间增长。这种共振的相互作用可能会在几小时内对海浪的光谱产生明显的改变。在本文中，通过一种稍微不同的方法，详细计算了最简单的可能情况下的相互作用：当三个主波数中的两个相等（k3 = k1）时。发现当k1和k2平行或反平行时，除非k1 = k2，否则相互作用消失。通常，如果θ表示k1与k2之间的夹角，则当θ [eDot] 17°时，第三波随时间的增长速度最大；当θ [eDot] 24°时，随水平距离的生长速率最大。计算表明，在实验室中应该可以探测到三次波。
In a previous paper, Phillips (1960) showed that two or three trains of gravity waves may interact so as to produce a fourth (tertiary) wave whose wave-number is different from any of three primary wave-numbers k1, k2, k3, and whose amplitude grows in time. Such resonant interactions may produce an appreciable modification of the spectrum of ocean waves within a few hours. In this paper, by a slightly different method, the interaction is calculated in detail for the simplest possible case: when two of the three primary wave-numbers are equal (k3 = k1). It is found that, when k1 and k2 are parallel or antiparallel, the interaction vanishes unless k1 = k2. Generally, if θ denotes the angle between k1 and k2, the rate of growth of the tertiary wave with time is a maximum when θ [eDot ] 17°; the rate of growth with horizontal distance is a maximum when θ [eDot ] 24°. The calculations show that it should be possible to detect the tertiary wave in the laboratory.