Dynamics of Three-dimensional Nonlinear Internal Waves Over Topography

0072145 Akylas在自然界中产生内部重力波的一种常见机制是地形上的流动。 所提出的工作的目标是提高我们的理论理解，特别强调三维非线性扰动的产生机制。为此，将发展一种渐近理论来描述三维地形上的近均匀分层流产生的有限振幅扰动，这种地形在展向比在流向上更细长。 所提出的理论使人们有可能探索某些功能的完全非线性波-例如，如何波破碎的三维效果的影响-，虽然主要的地球物理学的兴趣，迄今为止，已经违抗理论治疗。此外，这里所采用的数学方法是不同于以往的研究，并承诺推进我们的理解，从数学的角度来看，以及非线性内波的传播。重力内波是在海洋，湖泊和大气中的共同特点。 它们的存在是由于这些自然流体中存在的密度分层，这是由于温度变化以及盐度（海洋）和压力（大气）的变化。 地球物理内波具有巨大的尺度，从几公里到几百公里，因此它们是决定当地天气模式和气候动态的重要因素也就不足为奇了。 拟议的工作将提供一个数学描述的生成内波的地形，模拟风的行动在山脉的大气或电流的流动在海底的窗台。重点放在特定的流动条件下，内波的产生是最激烈的，预计将发挥重要作用，在地球物理应用（例如，雷暴的发展）。

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).