Motion of Interface Between Two Fluids

两种流体之间的界面运动

• 批准号: 9801094
• 负责人: Sijue Wu
• 金额: $ 6.2万
• 依托单位: University of Iowa
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-07-01 至 2000-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9801094&HistoricalAwards=false
• 关键词: Motion; Interface; Between; Two; Fluids

Proposal: DMS-9801094 Principal Investigator: Sijue Wu Abstract: Wu will study the long time behavior of water waves, as well as the motion of a general two-layered fluid flow. To understand the long time behavior of a water wave, Wu would like to determine whether the free surface of such a wave remains non-self-intersecting and whether solutions of water wave problems exist for all time, given that the initial free surface of the water wave is a small perturbation of still water. To be more precise, she would like to characterize those initial free surfaces that guarantee the non-self-intersection of the free surface of a water wave for all time. She also wants to study the blow-up mechanism for those solutions of the water wave problem that fail to exist for all time. The methods used to tackle these problems arise from harmonic analysis and the theory of partial differential equations. They include: decay estimates, maximal principle arguments, and the construction of a self-similar solution to the problem. To understand the motion of the interface between any two superposed fluids, Wu intends to study such fundamental questions as the existence of solutions to the equation governing the motion and the singularity profiles of solutions. To achieve this goal, she hopes to adapt the methods in her earlier work on water waves to derive a quasilinear equation equivalent to the equation that describes the motion of the interface. The reason for this approach is that the equation which models the motion of a two-fluid interface is highly nonlinear. In general, one has a better understanding of quasilinear equations than of fully nonlinear equations. The proposed research is a continuation of the work started by Nalimov, Yosihara and Craig and later advanced by the principal investigator on the existence and uniqueness of solutions of water wave problems and the work of Sulem, Dochun and Robert, Caflisch and Orellana, and Ebin on the well-posedness of vortex sheet motion. Fluid waves, in numerous guises, are present in some of the most familiar experiences of daily life, from the jarring impact of loud noises on our eardrums to the soothing ebb and flow of surf at a beach. The rich variety of phenomena associated with wave motion have provided generations of physicists and mathematicians with an important and challenging research subject. The general problem of motion of the free interface of two superposed fluids has applications to a wide variety of concrete physical problems. It has been used to understand the mixing of fluids, the separation of boundary layers, the generation of sounds, and coherent structures in models of turbulence. The long term objective of the proposed work is to understand wave-breaking in surface waves and the singularity mechanism in vortex sheets, both topics that have significant ramifications for physics and engineering.

提案：DMS-9801094主要研究者：吴思爵 翻译后摘要：吴将研究水波的长时间行为，以及一般的两层流体流动的运动。为了理解水波的长期行为，吴想确定这样的波的自由表面是否保持非自相交，以及水波问题的解是否一直存在，假定水波的初始自由表面是静水的小扰动。更准确地说，她想表征那些初始的自由表面，保证所有时间的水波的自由表面的非自交。她还想研究水波问题的解的爆破机制，这些解不可能永远存在。用来解决这些问题的方法来自调和分析和偏微分方程理论。它们包括：衰减估计，最大原理参数，以及问题的自相似解决方案的建设。为了理解任何两个叠加流体之间的界面的运动，吴打算研究这样的基本问题，如运动方程的解的存在性和解的奇异性。为了实现这一目标，她希望在她早期的水波工作中采用这种方法来推导出一个与描述界面运动的方程等价的准线性方程。采用这种方法的原因是模拟两流体界面运动的方程是高度非线性的。一般来说，人们对拟线性方程的理解要比对完全非线性方程的理解好。拟议的研究是一个延续的工作开始由Nalimov，Yosihara和克雷格和后来先进的首席研究员的存在性和唯一性的解决方案的水波问题和工作的Sulem，Dochun和罗伯特，Caflisch和Orellana，和Ebin的涡面运动的适定性。 流体波以多种形式出现在我们日常生活中最熟悉的一些体验中，从巨大噪音对我们耳膜的刺耳冲击到海滩海浪的舒缓起伏。与波动相关的各种现象为几代物理学家和数学家提供了一个重要而具有挑战性的研究课题。两种叠加流体自由界面运动的一般问题可应用于各种具体的物理问题。它已被用来理解流体的混合，边界层的分离，声音的产生，以及湍流模型中的相干结构。拟议工作的长期目标是了解表面波中的破波和涡面中的奇异性机制，这两个主题对物理和工程都有重要的影响。