Parasitic capillary waves: a direct calculation
Parasitic capillary waves: a direct calculation
复制标题
寄生毛细波：直接计算
DOI：
--
复制
发表时间：
1995
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
在以前的理论（Longuet-Higgins 1963）中，寄生毛细波被认为是由于表面张力对纯粹的前进重力波的局部作用而引起的扰动。这里的理论是改进：（i）利用我们更准确的知识，一个陡峭的斯托克斯波的轮廓;（ii）考虑到重力对毛细波本身的影响，通过有效的重力加速度g* 的短波骑在长波。不包括毛细管波本身的非线性，并进行某些其他近似。然而，理论与考克斯（1958）、江渊川村和鸟羽（1987）以及林林和丁（1993）的实验基本一致。一个主要结果是，对于给定长度L > 5 cm的重力波，存在一个临界陡度参数（AK）c，在该参数下表面速度（在与相速度一起移动的参考系中）等于毛细重力波的最小（局部）速度。在陡度AK <（AK）c的亚临界重力波中，可以在波面的所有点上产生毛细波。在超临界波上，当AK >（AK）c时，毛细波只能在波谷中产生;它们被困在波峰附近的两个焦散线之间。一般来说，寄生毛细管的振幅是最大的重力波附近的临界（但不是最大）陡度。
As in a previous theory (Longuet-Higgins 1963) parasitic capillary waves are considered as a perturbation due to the local action of surface tension forces on an otherwise pure progressive gravity wave. Here the theory is improved by: (i) making use of our more accurate knowledge of the profile of a steep Stokes wave; (ii) taking account of the influence of gravity on the capillary waves themselves, through the effective gravitational acceleration g* for short waves riding on longer waves. Nonlinearity in the capillary waves themselves is not included, and certain other approximations are made. Nevertheless, the theory is shown to be in essential agreement with experiments by Cox (1958), Ebuchi, Kawamura & Toba (1987) and Perlin, Lin & Ting (1993). A principal result is that for gravity waves of a given length L > 5 cm there is a critical steepness parameter (AK)c at which the surface velocity (in a frame of reference moving with the phase-speed) equals the minimum (local) speed of capillary-gravity waves. On subcritical gravity waves, with steepness AK < (AK)c, capillary waves may be generated at all points of the wave surface. On supercritical waves, with AK > (AK)c, capillary waves can only be generated in the wave troughs; they are trapped between two caustics near the crests. Generally, the amplitude of the parasitic capillaries is greatest on gravity waves of near critical (but not maximum) steepness.