有限水深三维海洋表面张力波-重力波之六波共振的 Hamilton波湍流理论体系

Starting from the Hamilton canonical equations for ocean surface waves and according to both the symmetry and the resonance conditions, a deterministic Zakharov equation for six-wave resonances of three dimensional ocean surface capillary-gravitational waves in water of finite depth is developed by way of a canonical transformation. By an ensemble averaging on it, a statistical Hasselmann equation is established, therefore leading to its Kolmogorov-Zakharov spectrum of the stationary solution. As view of extraordinary nonlocality, a series of the resonance conditions, the equations, the spectra and the experimental results for quasi-1D multi-wave resonances can be examined and interpreted, thus making a widely thorough interpretation and prediction of the evolution mechanism in wide freak waves with extraordinary elevations and extreme destructiveness concerned greatly in the ocean world . A more complete, practical and reliable theoretical hierarchy of six-wave resonances for Hamiltonian ocean surface wave turbulences is currently founded with the aid of the above-mentioned the Zakharov equation, the Hasselmann equation, the Kolmogorov-Zakharov spectrum, the nonlocality and the symmetry. The theoretical hierarchy can greatly enrich and promote the intension and standard of the extreme universal wave turbulence theories, and have surely a significant applicative prospect and value in extensive ocean engineering.

从海洋表面波的Hamilton正则方程出发，依据“对称性和波共振”条件，通过正则变换建立“确定性描述的有限水深三维海洋表面张力波-重力波之六波共振的Zakharov方程。”对其做系综平均，建立“统计描述的Hasselmann 方程”，并得到其定常解的Kolmogorov-Zakharov谱。以非比寻常的非局域性观点审视、解读准一维多波共振的一系列“共振条件、方程、谱和实验结果”，据此对海洋界极为关注、普遍的具有超常波高和极大破坏性的畸形波演变机制做一广为深入的解读、预测。上述“Zakharov 方程，Hasselmann 方程，Kolmogorov-Zakharov谱，非局域性，对称性”，即构建了一个目前更为完备、实际、可靠的六波共振的Hamilton海洋表面波湍流理论体系。以此，可大大丰富、提升具有极大普适性的波湍流理论的内涵和水准，必将在广泛的海洋工程领域里拥有可观的应用前景和价值。

本项目的主体研究目标业已完成。即构建了一个目前最为完备、可靠的4-5-6-波共振的Hamilton海洋表面重力波的湍流理论体系，以“动理学方程、Kolmogorov- Zakharov-型谱及其稳定性、Zakharov-型方程、3-4-5-6-波共振条件及其推广的n-波的共振条件”等为典型标志。以此，可有效提升具有极大普适性的波湍流理论的研究内涵和水准，为波在更为实际的非均匀介质中传播的波湍流后续工作奠定了一个必备、宽阔的研究基础，也必将在广泛的海洋工程领域里拥有可观的应用前景和价值。