Evolution of Obliquely Interacting Wavetrains in Deep Water

深水中倾斜相互作用波列的演化

• 批准号: 9972210
• 负责人: Diane Henderson
• 金额: $ 31.8万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-09-01 至 2003-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9972210&HistoricalAwards=false
• 关键词: Evolution; Obliquely; Interacting; Wavetrains; Deep

9972210The investigators conduct analytical, numerical, and experimental studies of three-dimensional water waves. They construct a state-of-the-art, precisely controlled, experimental facility that will enable the generation of nonlinear, three-dimensional wavefields and the direct measurement of their surface patterns. The goal is to use experiments to test and guide development of theoretical models and thereby obtain a unified experimental, theoretical, and numerical understanding of the evolution of nonlinear, three-dimensional surface waves over deep water. In particular they study (1) the dynamics of two obliquely interacting Stokes wavetrains, and (2) the dynamics of many obliquely interacting Stokes wavetrains that form resonantly interacting quartets.The investigators are building a precision facility in which to generate three-dimensional water waves with any desired shape, speed and complexity. One reason for these experiments is that an understanding of the fundamental physics of such waves greatly enhances the ability to model ocean waves. Models of ocean waves are necessary for a variety of applications, including shipping, construction, and defense. Models presently in use rest upon some mathematical assumptions that have never been tested and are possibly incorrect. The experiments of this project are designed to test these assumptions. A second reason for these experiments is that water waves are a physical application of the solutions to a special class of partial differential equations. These equations arise in many fields: oceanography, meteorology, plasma physics, and optics. Water waves provide a manageable experiment in which to study the application of the mathematics and to test the underlying assumptions and regimes of validity. If these equations model well the water wave experiments, then investigators in many fields have more confidence in applying them to other fields and in developing more such models. The project is supported by the Applied Mathematics and Computational Mathematics programs in the Division of Mathematical Sciences and by the Physical Oceanography program in the Division of Ocean Sciences.

9972210研究人员对三维水波进行分析、数值和实验研究。 他们建造了一个最先进的，精确控制的实验设施，将能够产生非线性，三维波场和直接测量其表面图案。 目标是用实验来测试和指导理论模型的发展，从而获得一个统一的实验，理论和数值理解的非线性，三维表面波的深水演变。 特别是他们研究（1）两个倾斜相互作用的斯托克斯波列的动力学，以及（2）形成共振相互作用的四元组的许多倾斜相互作用的斯托克斯波列的动力学。研究人员正在建造一个精确的设备，在其中生成具有任何期望形状，速度和复杂性的三维水波。 这些实验的一个原因是，对这种波浪的基本物理学的理解大大提高了模拟海浪的能力。 海浪模型对于各种应用都是必要的，包括航运，建筑和国防。 目前使用的模型依赖于一些从未经过测试的数学假设，而且可能是不正确的。 本项目的实验旨在验证这些假设。 这些实验的第二个原因是水波是一类特殊偏微分方程的解的物理应用。 这些方程出现在许多领域：海洋学，气象学，等离子体物理学和光学。 水波提供了一个可管理的实验，在其中研究数学的应用，并测试基本假设和有效性制度。 如果这些方程很好地模拟了水波实验，那么许多领域的研究人员就有信心将它们应用到其他领域，并开发更多这样的模型。 该项目由数学科学部的应用数学和计算数学计划以及海洋科学部的物理海洋学计划提供支持。