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.

该项目研究流体中的三维非线性重力 - 毛细血管的理论，下面是由刚性水平底部及以上自由表面的理论。 该研究集中在不可压缩的恒定密度的不可压缩流体上，并在重力和表面张力在自由表面的影响下移动，并以无关流动。 工作集中在三个问题领域。 第一个将建立精确的双 - 索顿溶液的存在，并倾斜相同的二维孤立波。 第二个区域的工作旨在证明存在三维传播波，这些波浪在水面张力较大的水中的繁殖和横向方向上都衰减至零。 第三个问题区域涉及存在来自二维广义孤立波的三维传播波，这是一个孤立的波浪，在无穷大的涟漪中，在具有小的表面张力的水中。 在这项工作中，使用确切的完全非线性的管理方程而不是近似模型方程来研究水中的三维传播表面波。 理论流体动力学和应用分析的相互作用对于项目至关重要。水波理论对于理解和控制许多重要的自然现象至关重要，例如风或地震产生的海浪以及船只产生的波。 该项目着重于三维水波的数学理论。 这项研究将有助于设计具有显着降低波动性的船舶，并了解实验中观察到的水波现象。 具有低波动性的船舶的设计对于消除快速渡轮产生的巨波尤其重要，该船只威胁着海岸线，并被归咎于许多船舶事故。