The equilibrium dynamics and statistics of gravity–capillary waves
The equilibrium dynamics and statistics of gravity–capillary waves
复制标题
重力-毛细波的平衡动力学和统计
DOI：
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发表时间：
2015
影响因子：
3.7
通讯作者：
A. Fedorov
中科院分区：
文献类型：
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作者：
W. Melville;A. Fedorov
摘要最近的野外观测和破碎表面重力波的模拟表明，对于波长为O（10）$ cm的较短重力波，空气夹带破碎对表面重力波的耗散不足以平衡风浪增长和非线性相互作用的动力学。在较短的陡峭重力波的波峰和前表面形成的寄生毛细波的理论表明，这些波的耗散效应可能比底层重力波的粘性耗散大一到两个数量级。因此，寄生毛细管可以提供所需的短的风产生的重力波的耗散。这一直是文献中推测和猜测的主题。使用Fedorov和梅尔维尔（J. Fluid Mech.，第354卷，1998年，第354页。1-42），我们表明，由于寄生毛细管的耗散是足够的，以平衡风输入的短重力波在一定范围内的波龄和波斜率。这些寄生毛细波动态显着的重力波长范围大致对应于考克斯和蒙克（J. Mar. Res.，第13卷，1954年，第13页。198-227）发现对海洋表面的均方斜率有很大的贡献，他们测量到海洋表面的均方斜率与风速成正比。在这里，我们表明，由理论预测的均方斜率是成比例的风的摩擦速度的平方，${u_{\ast }}^{2}$，对于小波浪的斜坡，和大约$u_{\ast }$较大的斜坡。
Abstract Recent field observations and modelling of breaking surface gravity waves suggest that air-entraining breaking is not sufficiently dissipative of surface gravity waves to balance the dynamics of wind-wave growth and nonlinear interactions with dissipation for the shorter gravity waves of $O(10)$ cm wavelength. Theories of parasitic capillary waves that form at the crest and forward face of shorter steep gravity waves have shown that the dissipative effects of these waves may be one to two orders of magnitude greater than the viscous dissipation of the underlying gravity waves. Thus the parasitic capillaries may provide the required dissipation of the short wind-generated gravity waves. This has been the subject of speculation and conjecture in the literature. Using the nonlinear theory of Fedorov & Melville (J. Fluid Mech., vol. 354, 1998, pp. 1–42), we show that the dissipation due to the parasitic capillaries is sufficient to balance the wind input to the short gravity waves over some range of wave ages and wave slopes. The range of gravity wave lengths on which these parasitic capillary waves are dynamically significant approximately corresponds to the range of short gravity waves that Cox & Munk (J. Mar. Res., vol. 13, 1954, pp. 198–227) found contributed significantly to the mean square slope of the ocean surface, which they measured to be proportional to the wind speed. Here we show that the mean square slope predicted by the theory is proportional to the square of the friction velocity of the wind, ${u_{\ast }}^{2}$ , for small wave slopes, and approximately $u_{\ast }$ for larger slopes.