Abstract In this article we study the time evolution of broad banded, random inhomogeneous fields of deep water waves. Our study is based on solutions of the equation derived by Crawford, Saffman and Yuen in 1980, (Crawford et al., 1980). Our main result is that there is a significant increase in the probability of freak wave occurrence than that predicted from the Rayleigh distribution. This result follows from the investigation of three related aspects. First, we study the instability of JONSWAP spectra to inhomogeneous disturbances whereby establishing a wider instability region than that predicted by Alber’s equation. Second, we study the long time evolution of such instabilities. We observe that, during the evolution, the variance of the free surface elevation and thus, the energy in the wave field, localizes in regions of space and time. Last, we compute the probabilities of encountering freak waves and compare it with predictions obtained from Alber’s equation and the Rayleigh distribution.

中文翻译：

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CSY 方程的新解揭示了异常波发生的增加

摘要 在本文中，我们研究了深水波的宽带、随机非均匀场的时间演化。我们的研究基于 Crawford、Saffman 和 Yuen 于 1980 年导出的方程的解（Crawford 等，1980）。我们的主要结果是，与根据瑞利分布预测的概率相比，异常波发生的概率显着增加。这个结果是从三个相关方面的调查得出的。首先，我们研究了 JONSWAP 谱对非均匀扰动的不稳定性，从而建立了比阿尔伯方程预测的更宽的不稳定性区域。其次，我们研究了这种不稳定性的长期演变。我们观察到，在演化过程中，自由表面高程的变化以及波场中的能量局部化在空间和时间区域。