Recurrent solutions of the Alber equation initialized by Joint North Sea Wave Project spectra
Recurrent solutions of the Alber equation initialized by Joint North Sea Wave Project spectra
复制标题
由联合北海波浪项目谱初始化的 Alber 方程的循环解
DOI：
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发表时间：
2013
影响因子：
3.7
通讯作者：
M. Stiassnie
中科院分区：
文献类型：
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作者：
A. Ribal;A. Babanin;Ian R. Young;A. Toffoli;M. Stiassnie
本文利用深水窄带随机表面波的阿尔伯方程，研究了非均匀扰动作用下二维波场的线性不稳定性及其随时间的同步演化。在这些模拟的背景下，畸形波的概率进行了讨论。首先研究了对称Lorentz谱的不稳定性，并继续为现实的非对称联合北海波浪计划（JONSWAP）谱的海洋波浪与可变的方向传播和陡度。结果表明，不稳定性取决于JONSWAP谱的方向扩展和参数$alpha $和$gamma $，其中$alpha $和$gamma $分别是能量尺度和峰值增强因子。两者都影响具有这种频谱的波的平均陡度，尽管方式不同。具体地说，如果不稳定性停止的结果，定向传播，通过增加$alpha $或$gamma $的陡度的增加可以重新激活它。不稳定性的标准建议作为一个无量纲的“宽度参数”，$Pi $。对于不稳定条件，通过数值积分阿尔伯方程来模拟长时间演化。递归演化，这是一个随机对应的费米-Pasta-Ulam递归立方薛定谔方程。这种递归使我们能够研究畸形波的概率，并将结果与瑞利分布给出的值进行比较。此外，它被发现，稳定不稳定的转变，最不稳定的模式，复发持续时间和畸形波的概率只依赖于无量纲的“宽度参数”，$Pi $。
Abstract Linear instability of two-dimensional wave fields and its concurrent evolution in time is here investigated by means of the Alber equation for narrow-banded random surface waves in deep water subject to inhomogeneous disturbances. The probability of freak waves in the context of these simulations is also discussed. The instability is first studied for the symmetric Lorentz spectrum, and continued for the realistic asymmetric Joint North Sea Wave Project (JONSWAP) spectrum of ocean waves with variable directional spreading and steepness. It is found that instability depends on the directional spreading and parameters $alpha $ and $gamma $ of the JONSWAP spectrum, where $alpha $ and $gamma $ are the energy scale and the peak enhancement factor, respectively. Both influence the mean steepness of waves with such a spectrum, although in different ways. Specifically, if the instability stops as a result of the directional spreading, increase of the steepness by increasing $alpha $ or $gamma $ can reactivate it. A criterion for the instability is suggested as a dimensionless ‘width parameter’, $Pi $ . For the unstable conditions, long-time evolution is simulated by integrating the Alber equation numerically. Recurrent evolution is obtained, which is a stochastic counterpart of the Fermi–Pasta–Ulam recurrence obtained for the cubic Schrödinger equation. This recurrence enables us to study the probability of freak waves, and the results are compared to the values given by the Rayleigh distribution. Moreover, it is found that stability–instability transition, the most unstable mode, recurrence duration and freak wave probability depend solely on the dimensionless ‘width parameter’, $Pi $ .