统一波浪模型及有限水深尖峰孤立波研究

The so-called “unified wave model” (UWM) proposed in 2013 by Prof. Shijun Liao, the PI of this proposal, can unify both of the smooth travelling waves and the peaked/cusped solitary waves, for the first time. In fact, it is the UWM which can give, for the first time, the peaked/cusped solitary waves in finite water depth, too. In this proposal, both of the smooth and peaked/cusped waves will be investigated as a whole in the frame of the “unified wave model” and the Navier-Stokes equations. Especially, the characteristics of the peaked/cusped solitary waves, the interactions between the peaked/cusped waves, the mechanism of their formation, the influence of the viscosity on the peaked/cusped solitary waves and so on, will be studied in details by means of analytical, numerical and experimental methods. This work will modify the so-called “unified wave model” and greatly deepen and enrich our understandings about the peaked/cusped solitary waves in finite water depth.

申请人2013年提出“统一波浪模型”，首次将传统光滑波浪和具有尖峰的非光滑波浪统一在一个理论框架下，首次获得有限深水中的尖峰孤立波。本申请进一步深入研究“统一波浪模型”，在一个更大、更一般的框架下，将光滑波浪和非光滑波浪作为一个整体进行研究，以解析近似、数值模拟和物理实验为研究手段，深入透彻地了解有限水深非光滑孤立波之性质、相互作用、形成机理，掌握粘性对有限水深非光滑孤立波之影响，完善“统一波浪模型”，丰富和发展非线性波浪理论。

项目负责人2013年提出“统一波浪模型”，首次将传统光滑波浪和具有尖峰的非光滑波浪统一在一个理论框架下，首次获得有限深水中的尖峰孤立波。并且，与传统的尖峰波方程不同，“统一波浪理论”能提供详细的二维流场，这为应用Navier-Stokes方程数值模拟尖峰孤立波提供了可能。本项目充分利用“统一波浪模型”，以理论求解、数值模拟和实验观察为手段，得到了诸多关键结论：有限水深中存在两类尖峰孤立波，不同尖峰孤立波具有密切的联系，理论上在任意水深中光滑波波高趋于极值时都可以演化为尖峰波，而尖峰波在特定参数下都可以演变为传统光滑孤立波，实验中还观察到了局部的尖峰波。所有结果都加深了对尖峰孤立波的理解，进一步丰富了非线性波浪理论。