Attenuation of short surface waves by the sea floor via nonlinear sub-harmonic interaction
Attenuation of short surface waves by the sea floor via nonlinear sub-harmonic interaction
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DOI：
10.1017/jfm.2011.448
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发表时间：
2011-11
影响因子：
3.7
通讯作者：
Mohammad-Reza Alam;Yuming Liu;D. Yue
中科院分区：
文献类型：
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作者：
Mohammad-Reza Alam;Yuming Liu;D. Yue
摘要我们考虑了短表面波通过与被底部耗散的长次谐波的近共振相互作用而耗散的间接机制。利用直接微扰分析和能量守恒，我们得到了两个短主波和长次谐波的振幅演化的解析预测，这两个短波和长次谐波构成了一个近共振的三和弦，阐明了从短波到长波的能量转移，这可能是随着时间的推移而意义重大的。我们得到了系统总能量损失率的表达式，并证明了该损失率存在一个极值，该极值对应于(底部)阻尼系数的一个特定值(对于给定的一对短波长相对于水深)。这些分析结果与针对一般非线性波-浪和波-底相互作用问题的直接数值模拟结果非常吻合。
Abstract We consider the indirect mechanism for dissipation of short surface waves through their near-resonant interactions with long sub-harmonic waves that are dissipated by the bottom. Using direct perturbation analysis and an energy argument, we obtain analytic predictions of the evolution of the amplitudes of two short primary waves and the long sub-harmonic wave which form a near-resonant triad, elucidating the energy transfer, from the short waves to the long wave, which may be significant over time. We obtain expressions for the rate of total energy loss of the system and show that this rate has an extremum corresponding to a specific value of the (bottom) damping coefficient (for a given pair of short wavelengths relative to water depth). These analytic results agree very well with direct numerical simulations developed for the general nonlinear wave–wave and wave–bottom interaction problem.