The dispersion of short wavelets in the presence of a dominant long wave
The dispersion of short wavelets in the presence of a dominant long wave
复制标题
在长波占主导地位的情况下短小波的色散
DOI：
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发表时间：
1981
影响因子：
3.7
通讯作者：
O. Phillips
中科院分区：
文献类型：
--
作者：
O. Phillips
本文研究了频率为N的长幅有限主波叠加并相互作用的短表面波的特性。渐近分析使Longuet-Higgins(1978)的数值研究扩展到更高的超谐扰动，并且发现，尽管重力子波被潜在的有限幅度波扭曲，但在主波不破裂的情况下，重力子波继续自由传播。然而，毛细管波可以被短的、陡峭的、不间断的重力波阻挡，因此在短距离和高风速的风浪水槽中，自由传播的重力-毛细管波可以被连续的主导波峰抹去。由于长波的应变，一列或一组短重力波在其局部波数上受到δk的调制，而在某一定点(其中C是长波相速)测得的视频率上受到大的调制Cδk，这主要是由于主波轨道速度产生的多普勒频移。波列的频谱特征是由驻相计算的，并发现在该范围内的上波数或频率处有极大值。如果在某一定点以给定频率f对一组短波群进行采样，则该信号来自固有频率范围为δ的群组，但由位于长波波峰的群组主导，其中f=δ+k.u0，其中u0是主波的轨道速度。一对这样的探头测得的视相速度是子波的传播速度c和长波的轨道速度u0之和。当f/N较大时，视相速度接近u0，与f无关。这些结果与Ramamonjiarisa&Giovanangeli(1978)等人的测量结果一致，其中发现高频下的视相速度与频率无关--因此，测量结果并不意味着海洋表面缺乏短重力波的频散。
The characteristics are studied of short surface waves superimposed upon, and interacting with, a long, finite-amplitude dominant wave of frequency N. An asymptotic analysis allows the numerical investigation of Longuet-Higgins (1978) to be extended to higher superharmonic perturbations, and it is found that, although they are distorted by the underlying finite-amplitude wave, gravity wavelets continue to propagate freely provided the dominant wave does not break. Capillary waves can, however, be blocked by short, steep, non-breaking gravity waves, so that in a wind-wave tank at short fetch and high wind speed, freely travelling gravity-capillary waves can be erased by the successive dominant wave crests. A train or group of short gravity waves suffers modulations δk in its local wave-number because of the straining of the long wave, and large modulations Cδk in its apparent frequency measured at a fixed point (where C is the long wave phase speed), largely because of the Doppler shifting produced by the dominant wave orbital velocity. The spectral signatures of a wave train are calculated by stationary phase and are found to have maxima at the upper wavenumber or frequency in the range. If an ensemble of short-wave groups is sampled at a given frequency f at a fixed point, the signal is derived from groups with a range of intrinsic frequencies δ, but is dominated by those at the long-wave crest for which f = δ + k.u0, where u0 is the orbital velocity of the dominant wave. The apparent phase speed measured by a pair of such probes is the sum of the propagation speed c of the wavelet and the orbital velocity u0 of the long wave. When f/N is large, the apparent phase speed approaches u0, independent of f. These results are consistent with measurements by Ramamonjiarisoa & Giovanangeli (1978) and others in which the apparent phase speed at high frequencies is found to be independent of the frequency — the measurements do not therefore imply a lack of dispersion of short gravity waves on the ocean surface.