Nonlinear Surface Waves on Water of Finite Depth

有限深度水面上的非线性表面波

• 批准号: 9971764
• 负责人: Shu-Ming Sun
• 金额: $ 7.5万
• 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: 1999
• 资助国家: 美国
• 起止时间: 1999-07-15 至 2003-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9971764&HistoricalAwards=false
• 关键词: Nonlinear; Surface; Waves; Water; Finite

9971764NONLINEAR SURFACE WAVES ON WATER OF FINITE DEPTHShu-Ming Sun The project concerns nonlinear capillary-gravity waves on water of finite depth. By ``water'', it means that an incompressible, inviscid fluid with constant density is moving under the influence of the gravity with surface tension on the free surface and the flow is irrotational. The proposed research focuses on the mathematical theory of nonlinear capillary-gravity waves on water bounded by a rigid horizontal bottom and a free surface. It consists of two parts. The first part intends to give a mathematical proof of the existence of three-dimensional propagating waves bifurcating from a two-dimensional solitary wave with large surface tension. The second part deals with the motion of capillary-gravity waves on the free surface of water in a two-dimensional rectangular region. The theory of water waves plays a crucial role in the development of fluid mechanics. Apart from being important in various branches of engineering and applied sciences, many water-wave phenomena happen in every-day experience. Waves generated by ships in rivers or reservoirs and waves generated by wind or earthquakes in oceans are probably the most familiar examples. This work focuses on certain wave motions on the free surface of water in oceans or reservoirs and intends to give some conditions for generating certain kinds of waves and obtain the large-time behavior of these waves. The results obtained from this research may present explanations of some natural phenomena, such as wave propagation in oceans generated by earthquakes, and provide descriptions of some wave motions in reservoirs that can be observed. Such understanding of those wave motions in oceans or reservoirs can be used to predict certain natural phenomena for preventing human disasters caused by them as well as benefiting from them, such as generating more electricity.

9971764在有限的深度刺激太阳水上的nononilarear表面波涉及有限深度水上的非线性毛细血管重力波。通过``水''，这意味着具有恒定密度的不可压缩的无粘性流体在重力的影响下移动，表面张力在自由表面上，流动是无关的。拟议的研究重点是在刚性水平底部和自由表面界定的水上的非线性毛细血管毛皮波的数学理论。它由两个部分组成。第一部分旨在给出数学证明，表明存在三维传播波，该波从具有较大的表面张力的二维孤立波分叉。第二部分涉及在二维矩形区域中自由表面上毛细血管刺激波的运动。 水波理论在流体力学的发展中起着至关重要的作用。除了在工程和应用科学的各个分支中都很重要外，每天的体验中都会发生许多水波现象。河流中的船只产生的波浪或海洋中的河流和海浪产生的波浪可能是最熟悉的例子。这项工作着重于海洋或储层中水的自由表面的某些波动运动，并打算给出某些条件以产生某些波浪并获得这些波浪的大型行为。从这项研究中获得的结果可能介绍了某些自然现象的解释，例如地震产生的海洋中的波传播，并提供了可以观察到的储层中某些波动运动的描述。对海洋或水库中这些波动运动的理解可用于预测某些自然现象，以防止造成人类灾难并从中受益，例如产生更多的电力。