Wave Turbulence: Open Challenges and New Opportunities

波浪湍流：开放的挑战和新的机遇

• 批准号: 0072803
• 负责人: Vladimir Zakharov
• 金额: $ 16.1万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-08-01 至 2003-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0072803&HistoricalAwards=false
• 关键词: Wave; Turbulence; Open; Challenges; New

NSF Award Abstract - DMS-0072803Mathematical Sciences: Wave Turbulence -- Open Challenges and New OpportunitiesAbstract0072803 ZakharovWave turbulence, the turbulence of a sea of weakly-coupled dispersive wave trainsdriven far from equilibrium by sources and sinks, is ripe for renewed investigation.First, there are many open challenges which need to be addressed: the effectof discreteness in impeding spectral energy redistribution; the general nature ofanisotropic finite flux spectra in wind-driven oceans, in magnetohydrodynamics inthe presence of strong magnetic field, and in sound waves; the role of hidden constantsof the motion; the surprising manner in which finite capacity Kolmogorov spectraare realized; the modification of Fermi-Dirac (and Bose-Einstein) spectra in contextssuch as semiconductor lasing where finite flux effects are important. Second, thesubject is important because it provides tractable models which can be exploitedto gain insight into the phenomenon of intermittency. Because the approximationswhich underlie the applications of wave turbulence theory are generally not valid uniformly in wave number, there are windows of intermittency at both high and low wave number values. At these scales, the system is fully nonlinear and exhibits intermittent bursts of activity associated with coherent but almost singular structures. Our aim is to build a comprehensive theory which combines and connects wave turbulence with the random occurrence of coherent events.This project investigates the long-time statistical behavior of complex solutions to nonlinear field equations arising in a broad family of physical systems. Applications of the research include modeling of: wind-driven ocean waves, weather, laser beams in transparent materials, sound waves, solar wind and stellar atmospheres, and motion of charges in semiconductor lasers. All these systems exhibit turbulent behavior with common features, and the project develops the theory of this common structure. The goal is to gain understanding of the behavior of this family of physical systems as well as to study the general statistical behavior of nonlinear systems in which large fluctuations

美国国家科学基金会奖摘要- DMS-0072803数学科学：波浪湍流--开放的挑战和新的机遇摘要0072803 Zakharov波浪湍流，一个弱耦合色散波列的海洋湍流，被源和汇驱动远离平衡，是重新研究的成熟。首先，有许多需要解决的开放性挑战：离散性在阻碍谱能量重新分布中的作用;各向异性有限通量谱在风驱动海洋中、在强磁场存在下的磁流体力学中以及在声波中的一般性质;运动的隐藏常数的作用;有限容量Kolmogorov谱实现的令人惊讶的方式;费米-狄拉克（和玻色-爱因斯坦）谱在有限通量效应很重要的半导体激光等背景下的修改。 第二，这个主题很重要，因为它提供了易于处理的模型，可以利用这些模型来深入了解不连续性现象。 由于作为波动湍流理论应用基础的近似在波数上通常不是一致有效的，因此在高波数和低波数值上都存在不连续性窗口。 在这些尺度上，系统是完全非线性的，并表现出与连贯但几乎奇异的结构相关的间歇性活动爆发。 我们的目标是建立一个综合的理论，结合和连接波湍流与随机发生的相干事件。本项目研究的复杂的解决方案，非线性场方程的长时间的统计行为，产生在一个广泛的家庭的物理系统。 该研究的应用包括建模：风驱动的海浪，天气，透明材料中的激光束，声波，太阳风和恒星大气，以及半导体激光器中电荷的运动。 所有这些系统都表现出具有共同特征的湍流行为，该项目发展了这种共同结构的理论。 目标是了解这一系列物理系统的行为，以及研究大波动的非线性系统的一般统计行为。