FRG: Collaborative Research: Fully Nonlinear, Three-Dimensional Waves in Water of Arbitrary Depth

FRG：合作研究：任意深度水中的完全非线性三维波

• 批准号: 0139742
• 负责人: Harvey Segur
• 金额: $ 7.53万
• 依托单位: University of Colorado at Boulder
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-08-15 至 2005-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0139742&HistoricalAwards=false
• 关键词: FRG; Collaborative; Research; Fully; Nonlinear

The overall objectives of this work are to develop a thorough understanding of three-dimensional water waves of finite amplitude, and ultimately to develop a practical model to describe these waves efficiently. A model that is both accurate and computationally efficient could have many practical applications. Specific problems to be addressed are: (1) the existence and stability of three-dimensional, doubly-periodic, traveling water-wave patterns, through the full range of depths; (2) the prevalence of hexagonal, rectangular or crescent-shaped waves (or other multiply periodic wave patterns) among ocean waves; (3) the long-wave and modulational descriptions of water waves, and the subsequent stability analyses that are feasible in these cases; (4) the design and implementation of algorithms to make practical use of exact solutions of asymptotic models in shallow and deep water; (5) the relation between the detailed dynamics of three-dimensional, nonlinear waves and some commonly used ocean-wave transport models; and (6) the impact of a detailed local description of nonlinear wave dynamics on these transport models, in the presence of large amplitude nonlinear waves or under conditions of nonlinear wave focusing. These problems will be studied using analysis, computation, asymptotics, and algebraic geometry, involving the full equations and approximate models, all in conjunction with state-of-the-art physical experiments.The destructive force of large-amplitude ocean waves is well known. Large-scale ocean waves have a major impact on the design of ocean-going ships, of off-shore oil platforms, and of other structures in a coastal environment. These waves also impact the scheduling and routing of shipping patterns, and they strongly affect air-sea transport processes. Yet most theoretical models of ocean waves now in use are based on waves of small amplitude. In this investigation we focus on developing a thorough understanding of large-amplitude waves. The ultimate goal is to develop a practical, mathematical model that may be used operationally in the applications listed above. In particular, the investigators plan to build on their recent work in which they have observed certain coherent patterns of large-amplitude waves. They have observed these patterns in laboratory experiments, as solutions to the well-known equations of water waves, and as solutions to other equations that are (more) approximate models of water waves. Their work involves a variety of mathematical and computational tools as well as state-of-the-art laboratory experiments. In the present work the investigators will combine all of their tools to understand and describe these coherent patterns and to use them as the building blocks for a practical model of ocean waves.

这项工作的总体目标是对有限幅度的三维水波彻底理解，并最终开发一个实用模型来有效地描述这些波。一个既准确又具有计算高效的模型可以具有许多实际应用。要解决的具体问题是：（1）三维，双周期，行进的水波图案的存在和稳定性，穿过整个深度； （2）海浪中六角形，矩形或新月形波（或其他乘周期波模式）的流行； （3）水波的长波和调节描述，以及随后在这些情况下可行的稳定性分析； （4）算法的设计和实施，以实际利用浅水和深水中渐近模型的精确解决方案； （5）三维非线性波的详细动力学与一些常用的海浪传输模型之间的关系； （6）在存在大幅度非线性波或非线性波聚焦的条件下，非线性波动力学对非线性波动力学对这些传输模型的详细局部描述的影响。这些问题将使用分析，计算，渐近学和代数几何形状研究，涉及完整的方程式和近似模型，所有这些都与最新的物理实验结合在一起。大型海浪的破坏力是众所周知的。大规模的海浪对沿海环境中的海洋船舶，离岸油平台以及其他建筑物的设计产生了重大影响。 这些波还影响了运输方式的调度和路线，并且会严重影响空气运输过程。然而，目前正在使用的海浪的大多数理论模型都是基于小幅度的波。在这项调查中，我们着重于对大振幅波的全面理解。最终目标是开发一个实用的数学模型，该模型可以在上面列出的应用程序中使用。特别是，研究人员计划基于他们最近观察到的某些相干模式的大振幅波。他们已经在实验室实验中观察到这些模式，作为众所周知的水波方程的解决方案，以及（更多）（更多）近似水波模型的其他方程的解决方案。他们的工作涉及多种数学和计算工具以及最先进的实验室实验。在目前的工作中，调查人员将结合其所有工具，以理解和描述这些连贯的模式，并将它们用作海浪实用模型的基础。