Evolution of Obliquely Interacting Wavetrains in Deep Water

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、精确控制的实验设备，将能够产生非线性的三维波场，并直接测量其表面图案。其目的是利用实验来测试和指导理论模型的发展，从而获得对深水上非线性三维表面波演变的统一的实验、理论和数值理解。他们特别研究了(1)两个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个波列的许多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密的设备，在其中产生任何所需形状、速度和复杂性的三维水波。这些实验的一个原因是，对这种波的基本物理的理解大大增强了对海浪进行建模的能力。海浪模型在包括航运、建筑和国防在内的各种应用中都是必不可少的。目前使用的模型依赖于一些数学假设，这些假设从未经过测试，可能是错误的。本项目的实验就是为了验证这些假设。这些实验的第二个原因是，水波是对一类特殊偏微分方程解的物理应用。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，在其中学习数学的应用，并测试潜在的假设和有效性模式。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更有信心将它们应用于其他领域，并开发更多这样的模型。该项目得到了数学科学部的应用数学和计算数学方案以及海洋科学部的物理海洋学方案的支持。

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.