On resonant interactions of gravity-capillary waves without energy exchange
On resonant interactions of gravity-capillary waves without energy exchange
复制标题
关于无能量交换的重力-毛细波的共振相互作用
DOI：
10.1111/sapm.12249
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发表时间：
2019
影响因子：
2.7
通讯作者：
Choi, Wooyoung
中科院分区：
文献类型：
--
作者：
Chabane, Malik;Choi, Wooyoung
我们考虑重力-毛细波的共振三重波相互作用，并详细研究特殊的共振三重波，它们在相互作用期间不交换能量，因此波的振幅在时间上保持恒定。在用两个参数（或波传播的两个角度）写出谐振条件后，我们首先在二维参数空间中确定一个总是可以找到谐振三和弦的区域，然后描述谐振波数和波频率的变化谐振区域。使用恢复的振幅方程从哈密顿制定水波，它表明，任何共振三和弦内的共振区域可以相互作用，而没有能量交换，如果初始波的振幅和相对相位满足两个条件的振幅方程的不动点解。此外，它表明，不交换能量的对称共振三波形成横向调制行波场，这可以被认为是威尔顿波纹的二维推广。
We consider resonant triad interactions of gravity‐capillary waves and investigate in detail special resonant triads that exchange no energy during their interactions so that the wave amplitudes remain constant in time. After writing the resonance conditions in terms of two parameters (or two angles of wave propagation), we first identify a region in the two‐dimensional parameter space, where resonant triads can be always found, and then describe the variations of resonant wavenumbers and wave frequencies over the resonance region. Using the amplitude equations recovered from a Hamiltonian formulation for water waves, it is shown that any resonant triad inside the resonance region can interact without energy exchange if the initial wave amplitudes and relative phase satisfy the two conditions for fixed point solutions of the amplitude equations. Furthermore, it is shown that the symmetric resonant triad exchanging no energy forms a transversely modulated traveling wave field, which can be considered a two‐dimensional generalization of Wilton ripples.