Dynamics of Three-dimensional Nonlinear Internal Waves Over Topography

地形上三维非线性内波动力学

• 批准号: 0072145
• 负责人: Triantaphyllos Akylas
• 金额: $ 12.4万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-09-01 至 2004-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0072145&HistoricalAwards=false
• 关键词: Dynamics; Three; dimensional; Nonlinear; Internal

0072145AkylasA common mechanism by which internal gravity waves are generated in nature is flow over topography. The goal of the proposed work is to improve our theoretical understanding of this generation mechanism with particular emphasis on three-dimensional nonlinear disturbances. To this end, an asymptotic theory will be developed to describe the generation of finite-amplitude disturbances by nearly uniformly stratified flow over three-dimensional topography that is more elongated in the spanwise than in the streamwise direction. The proposed theory makes it possible to explore certain features of fully nonlinear waves --- for instance, how wave breaking is influenced by three-dimensional effects --- that, although of primary geophysical interest, so far have defied theoretical treatment. Moreover, the mathematical approach taken here is distinct from prior studies and promises to advance our understanding of nonlinear internal wave propagation from a mathematical standpoint as well.Internal gravity waves are common features in oceans, lakes and in the atmosphere. They owe their existence to the density stratification present in these natural fluid bodies due to variations in temperature and changes in the salinity (in the case of oceans) and pressure (in the case of the atmosphere). Geophysical internal waves are known to possess enormous scales, on the order of kilometers to hundreds of kilometers, so it is not surprising that they are important factors in determining local weather patterns and climate dynamics. The proposed work will provide a mathematical description of the generation of internal waves by flow over topography, modeling the action of wind over mountain ranges in the atmosphere or the flow of currents over a sill in the ocean bottom. Emphasis is placed on particular flow conditions under which internal-wave generation is most violent and is expected to play an important part in geophysical applications (e.g., the development of thunderstorms).

0072145 akylas自然界中产生内部重力波的一个常见机制是在地形上流动。提出的工作的目标是提高我们对这种产生机制的理论理解，特别强调三维非线性扰动。为此，将发展一种渐近理论来描述三维地形上几乎均匀分层的流动产生的有限振幅扰动，这种地形在展向上比在流向上更拉长。提出的理论使探索完全非线性波的某些特征成为可能——例如，波浪破碎如何受到三维效应的影响——尽管主要是地球物理学的兴趣，但迄今为止还没有得到理论处理。此外，这里采用的数学方法与以前的研究不同，并有望从数学的角度推进我们对非线性内波传播的理解。内部重力波是海洋、湖泊和大气中的常见特征。它们的存在是由于这些天然流体体由于温度变化和盐度（在海洋中）和压力（在大气中）的变化而产生的密度分层。众所周知，地球物理内波具有巨大的尺度，在公里到数百公里之间，因此它们是决定当地天气模式和气候动力学的重要因素也就不足为奇了。这项提议的工作将对地形上的气流产生的内波提供数学描述，模拟大气中山脉上的风的作用或海底海底海底的水流。重点放在特定的流动条件下，在这种条件下内波的产生是最剧烈的，预计将在地球物理应用中发挥重要作用（例如，雷暴的发展）。