Collaborative Research: Nonlinear Water Waves

合作研究：非线性水波

• 批准号: 1107354
• 负责人: Harvey Segur
• 金额: $ 15.1万
• 依托单位: University of Colorado at Boulder
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-06-15 至 2015-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1107354&HistoricalAwards=false
• 关键词: Collaborative; Research; Nonlinear; Water; Waves

Many physical systems admit nonlinear waves. These systems often exhibit dissipation that is considered to be negligible or weak. However, recent work by the investigators and recently published observations of dissipation rates of ocean swell, show that the models using weak dissipation provide an inadequate description of some aspects of the evolution of nonlinear surface water waves. Thus, a main emphasis of this research is to develop a theory from first principles for the propagation and evolution of nonlinear surface water waves on a viscous fluid, with no approximation on the size of dissipation. The research addresses several projects that build on this notion and/or are intended to apply the mathematical results to ocean applications. The projects fall into two categories: A) surface waves propagating on a viscous fluid and B) waves in shallow or finite-depth water. The investigators will approach these problems by combining their individual strengths in modeling and analysis, numerical simulations, and physical experiments to obtain a fundamental mathematical description of the physical phenomena. They will then use publicly available data from ocean observations to apply their results to ocean settings.The primary goal of this research is to understand at a fundamental, mathematical level the propagation of waves on a surface of water, and to apply this understanding to observations of waves measured in the laboratory and in the oceans. Particular applications include the effects of dissipation on the generation of waves by wind, the subsequent propagation of ocean swell, and the development of rogue waves in shallow and deep water; predicting dangerous versus benign tsunamis given the Richter-scale measure of the magnitude of the responsible earthquake and some readily available information about the geology of its location; and modeling large-amplitude waves on beaches with variable bathymetry using the new mathematical approaches investigated here. In addition, the mathematical results are expected to describe nonlinear waves in several settings, including light waves in an optical fiber, spin waves in a thin magnetic film and others. Graduate and undergraduate students will be mentored and involved in experimental studies and theoretical analysis; through this project they will receive training in interdisciplinary research.

许多物理系统都承认非线性波。这些系统通常表现出可忽略不计或较弱的耗散。然而，研究人员最近的工作和最近发表的对海洋涌浪耗散率的观测结果表明，使用弱耗散的模型不能充分描述非线性表面水波演化的某些方面。因此，这项研究的主要重点是根据粘性流体上非线性表面水波的传播和演化的第一原理发展一种理论，而不需要近似耗散的大小。该研究涉及基于这一概念和/或旨在将数学结果应用于海洋应用的几个项目。这些项目分为两类：A）在粘性流体上传播的表面波和 B）浅水或有限深度水中的波。研究人员将通过结合各自在建模和分析、数值模拟和物理实验方面的优势来解决这些问题，以获得物理现象的基本数学描述。然后，他们将使用来自海洋观测的公开数据，将其结果应用于海洋环境。这项研究的主要目标是从基础的数学层面了解波浪在水面上的传播，并将这种理解应用于观测在实验室和海洋中测量的波浪。具体应用包括耗散对风产生的波浪的影响、随后的海浪传播以及浅水和深水中的异常波浪的发展；根据引发地震震级的里氏震级测量值以及有关地震所在地地质的一些现成信息，预测危险海啸与良性海啸；并使用此处研究的新数学方法，通过可变测深法对海滩上的大幅波浪进行建模。此外，数学结果有望描述多种设置中的非线性波，包括光纤中的光波、磁性薄膜中的自旋波等。研究生和本科生将接受指导并参与实验研究和理论分析；通过该项目，他们将接受跨学科研究的培训。