Energy balance in a wind-driven sea
Energy balance in a wind-driven sea
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风驱动海洋中的能量平衡
DOI：
10.1088/0031-8949/2010/t142/014052
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发表时间：
2010
期刊：
影响因子：
2.9
通讯作者：
V. Zakharov
中科院分区：
文献类型：
--
作者：
V. Zakharov
在本文中，我们给出了一些问题的答案，这些问题对发展自洽的风海分析理论非常重要。(1)讨论了深水表面弱非线性重力波系综中“共振”谐波和“从”谐波的分离，并构造了消除从谐波的正则变换生成函数的显式形式。（ii）当组成一个四波的两个波比其他两个波短时，我们找到了四波耦合系数的渐近形式。这一结果使得将哈塞曼方程简化为非线性扩散方程成为可能，其解描述了众所周知的波谱在其背面的角扩散效应。(3)研究了Hasselmann方程的各向同性Kolmogorov - zakharov解，求得了Kolmogorov常数的数值。（iv）计算了由于四波相互作用而产生的表面波的非线性阻尼，并将阻尼与风引起的波面不稳定性的增长率进行了比较。研究发现，对于所有已知的风输入模型，非线性阻尼至少在数量级上超过不稳定性。这一结果得到了哈塞曼方程数值模拟的支持，由此得出结论：在真实的海洋中，除了非常年轻的波浪外，四波相互作用是主要的过程。这一说法为海风驱动的海洋的合理分析理论的发展开辟了道路。
In this paper, we offer the answers to certain questions extremely important for the development of a self-consistent analytical theory for the wind-driven sea. (i) We discuss the separation into ‘resonant’ and ‘slave’ harmonics in an ensemble of weakly nonlinear gravity waves on the surface of deep water, and we construct an explicit form of the generation function for canonical transformation that eliminates the slave harmonics. (ii) When two waves compiling a quadruple are short in comparison with two others, we find an asymptotic form for the four-wave coupling coefficient. This result makes it possible to reduce the Hasselmann equation to the nonlinear diffusion equation, whose solution describes the well-known effect of angular spreading of wave spectra on its rear face. (iii) Studying the isotropic Kolmogorov–Zakharov solution of the Hasselmann equation, we find numerically the values of Kolmogorov constants. (iv) We calculate the nonlinear damping of surface waves appearing due to four-wave interaction and compare the damping with the growth rate of the instability of the wave surface induced by the wind. It is found that for all known models of wind input, the nonlinear damping surpasses the instability at least in order of magnitude. This result, supported by numerical simulation of the Hasselmann equation, leads to the conclusion: in a real sea, except for the case of very young waves, four-wave interaction is the dominant process. This statement opens the way for the development of a well-justified analytical theory for the wind-driven sea.