Benjamin-Ono方程中随机场的演化与统计分析
Evolution and statistical analysis of random wave fields within the Benjamin-Ono equation
AI总结：
基于Benjamin-Ono方程模拟高斯谱初始内波随机场在不同Ursell参数下的演化，分析谱、统计矩、波幅分布及畸形波概率，发现非高斯统计特征和“两姐妹”“三姐妹”畸形波。
摘要：
本研究利用Benjamin-Ono（BO）方程研究了具有高斯谱形特征的初始内部随机场的数值演化。研究重点是分析与BO随机场相关的各种性质，包括向谱、统计矩和波幅分布函数的稳态转变。数值模拟在不同的Ursell参数下进行，揭示了有趣的发现。值得注意的是，观察到波场谱在统计意义上收敛到平稳状态，同时表现出偏离高斯分布的统计特征。此外，随着Ursell参数的增加，波场的正偏度增强，峰度增大。研究还涉及计算畸形波形成的概率，揭示了其与Rayleigh分布的偏差。值得注意的是，研究发现了不同类型的畸形波，具体称为“两姐妹”和“三姐妹”现象。
英文摘要：
This study investigates the numerical evolution of an initially internal random wave field characterized by a Gaussian spectrum shape using the Benjamin-Ono (BO) equation. The research focuses on analyzing various properties associated with the BO random wave field, including the transition to a steady state of the spectra, statistical moments, and the distribution functions of wave amplitudes. Numerical simulations are conducted across different Ursell parameters, revealing intriguing findings. Notably, it is observed that the spectra of the wave field converges to a stationary state in a statistical sense, while exhibiting statistical characteristics that deviate from a Gaussian distribution. Moreover, as the Ursell parameter increases, the positive skewness of the wave field intensifies, and the kurtosis increases. The investigation also involves the computation of the probability of rogue wave formation, revealing deviations from the Rayleigh distribution. Notably, the study uncovers distinct types of rogue waves, specifically referred to as "two sisters" and "three sisters" phenomena.
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