Three-Dimensional Nonlinear Gravity-Capillary Water Waves

三维非线性重力毛细管水波

• 批准号: 0309160
• 负责人: Shu-Ming Sun
• 金额: $ 11.6万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-08-01 至 2007-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0309160&HistoricalAwards=false
• 关键词: Three; Dimensional; Nonlinear; Gravity; Capillary

This project studies the theory of three-dimensional nonlinear gravity-capillary waves in fluid bounded below by a rigid horizontal bottom and above by a free surface. The research is focused on incompressible inviscid fluids of constant density, moving under the influence of gravity and surface tension on the free surface, with irrotational flow. The work centers on three problem areas. The first will establish the existence of exact twin-soliton solutions, obliquely-interacting identical two-dimensional solitary waves. Work in the second area aims to prove the existence of three-dimensional propagating waves that decay to zero in both propagating and transverse directions in water with large surface tension. The third problem area concerns the existence of three-dimensional propagating waves bifurcating from a two-dimensional generalized solitary wave, a solitary wave with ripples at infinity, in water with small surface tension. In this work, the exact fully nonlinear governing equations, rather than approximate model equations, are employed to study three-dimensional propagating surface waves in water. Interplay of theoretical fluid dynamics and applied analysis is essential to the project. The theory of water waves is essential for understanding and control of many important natural phenomena, such as ocean waves generated by wind or earthquakes, and waves generated by ships. This project focuses on the mathematical theory of three-dimensional water waves. The research will contribute to the design of ships with significantly reduced wave resistance, as well as understanding of water-wave phenomena observed in experiments. Design of ships with low wave resistance is especially important for eliminating giant waves generated by fast ferries, which threaten coastlines and have been blamed for many boat accidents.

本项目研究流体中三维非线性重力-毛细波理论，流体下方为刚性水平底，上方为自由面。研究的对象是等密度的不可压缩无粘流体，在重力和表面张力的影响下在自由表面上运动，具有无旋流。这项工作围绕三个问题领域展开。第一个将建立精确的孪生孤子解的存在性，即斜相互作用的完全相同的二维孤立波。第二个领域的工作旨在证明在具有大表面张力的水中，三维传播波的存在，该波在传播方向和横向都衰减为零。第三个问题涉及在具有小表面张力的水中存在从二维广义孤立波分叉出来的三维传播波，该孤立波在无穷远处具有波纹。本文采用精确的完全非线性控制方程，而不是近似的模型方程来研究三维表面波在水中的传播。理论流体力学和应用分析的相互作用对该项目至关重要。水波理论对于理解和控制许多重要的自然现象是必不可少的，例如风或地震产生的海浪，以及船舶产生的海浪。本项目主要研究三维水波的数学理论。这项研究将有助于显著降低波浪阻力的船舶的设计，以及对在实验中观察到的水波现象的理解。对于消除快速渡轮产生的巨浪来说，低抗浪船舶的设计尤为重要。快速渡轮威胁着海岸线，被指责为许多船只事故的罪魁祸首。