强流耦合高阶非线性畸形波数学模型与时频演化特性研究

A rogue wave is a type of very rare and extremely large wave that possesses powerful concentrated energy, strong nonlinear dynamics and can be enormously devastating. When it interacts with deep-sea structures, the structure’s integrity will suffer a potentially serious threat, its stability and orientation will be severely challenged and it may even cause significant harm to the on-board staff and valuable property. As the rogue waves were frequently observed in the areas with strong currents such as the Agulhas Current, the Gulf Stream and the Kuroshio Current, the accidents caused by the rogue wave events due to strong current have been paid much interest. Considering the effects of higher order nonlinearity and strong current on the evolution of the rogue wave, a modified mathematical model will be developed by using the multi-scale expand method. The wave tank test will be carried out to validate the mathematical model. Based on the modified mathematical model derived above, the nonlinear properties of the rogue wave evolution under the effects of strong current can be numerically calculated by the fourth-order split-step pseudo-spectral method. The wavelet analysis method is adapted to obtain the time-frequency spectrum and the wavelet auto-bicoherence spectrum, revealing the internal energy structure of the rogue waves influenced by strong current. The statistical property of the rogue wave under the effect of the strong current is also investigated through extensive numerical simulation to obtain the probability density function, kurtosis, skewness and randomness.

畸形波是一种能量集中、非线性极强、破坏力极大的波浪，与深海结构物相互作用时，将对结构安全性构成严重威胁，对海上工作人员以及财产造成重大危害。近年来，多起畸形波导致的海南事故发生于强海流海域，如阿古拉斯海流，日本暖流和墨西哥湾流等，强海流引起的畸形波事件得到了国内外的广泛关注。本项目综合考虑强海流以及高阶非线性对波浪演化的影响,拟使用多重尺度方法建立强流耦合高阶非线性数学模型并利用水池实验进行验证。基于修正的强流耦合高阶非线性数学模型，通过四阶离散步长-虚拟波谱方法对呼吸子式畸形波的生成演化进行数值模拟，获得强流耦合作用下畸形波的非线性生成演化特性。利用小波分析手段，获得强流耦合作用下畸形波的时-频能量谱以及小波自相关函数,揭示其内部能量结构。通过大规模的数值模拟，对大流速下波流耦合对畸形波的统计特性进行深入研究，从概率分布函数，峰度，偏度，随机性等方面探究不同形式海流对畸形波统计特性的影响

畸形波多在偶然情况下发生，且经常出现在强逆流存在的海域（如南非东南沿海），因此，波流相互作用也被认为是畸形波的一个重要形成机理。本项目旨在从理论上揭示强流耦合作用下畸形波的非线性生成演化机制，根据畸形波的成因与特征，建立畸形波非线性数学模型，对四阶时间-空间薛定谔方程进行风修正，完成其数学模型的推导验证。正确描述强海流耦合作用下畸形波浪强非线性的时空变化特性，实现畸形波的数值模拟和实验室物理模拟。从能量结构的角度揭示畸形波的非线性波流耦合作用机理。基于非线性波浪理论，结合模型实验，考虑波浪参数变化，研究畸形波在强海流作用下的统计特性等，通过统计分析获得海流不同流速对畸形波的聚焦位置，波浪放大等特性的影响。探索了随机波在三维孤立礁地形上的传播方式，验证了在真实地形进行三维模型试验的有效性。最后提出了一种相位修正方法来修正数值仿真过程中的相位角，使得最终得到的理论计算结果与实验数据吻合较好，验证了提出的相位修正方法的可行性。为后续研究波浪-结构相互作用，如波浪砰击和爬高奠定了基础。