Nonlinear Wave Dynamics in Stratified Flows

层流中的非线性波动力学

• 批准号: 0305940
• 负责人: Triantaphyllos Akylas
• 金额: $ 18.1万
• 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: 2003
• 资助国家: 美国
• 起止时间: 2003-10-01 至 2007-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0305940&HistoricalAwards=false
• 关键词: Nonlinear; Wave; Dynamics; Stratified; Flows

Two problems of gravity wave propagation in stratified flows will be studied: the propagation of internal wave beams and the resonant interaction of nonlinear modulated wavetrains with the induced mean flow. Since gravity provides a preferred direction, internal wave disturbances generated by an oscillatory source are anisotropic; rather than cylindrical fronts, they form straight beams stretching radially outwards. The propagation characteristics of such beams will be studied under various flow conditions using asymptotic and numerical models. Particular emphasis will be placed on three-dimensional and non-axisymmetric beams for which nonlinear effects are most pronounced. Secondly, a theoretical study will be made of the so-called resonant self-acceleration of modulated wavetrains; this strong nonlinear interaction between the wavetrain envelope and the induced horizontal mean flow can cause instability and breakdown of nearly vertically propagating wavetrains. Although not as familiar from everyday experience as ocean surface waves, internal gravity waves are in fact ubiquitous in oceans, lakes and in the atmosphere, where they play an important part in transferring momentum and energy. Internal gravity wave beams in particular are often triggered by thunderstorms, and there is evidence from numerical simulations and field observations that a significant component of gravity wave activity in the atmosphere is in the form of beam-like structures. Understanding the propagation characteristics of internal gravity wave beams will thus prove useful in weather forecasting. This award is being jointly funded by the Division of Mathematical Sciences and the Directorate for Engineering as part of the Mathematical Sciences Priority Area.

本文将研究重力波在分层流中传播的两个问题：内波束的传播和非线性调制波列与诱导平均流的共振相互作用。由于重力提供了一个较好的方向，由振荡源产生的内波扰动是各向异性的；它们形成径向向外伸展的直束，而不是圆柱形锋面。我们将利用渐近模型和数值模型研究这类光束在不同流动条件下的传输特性。重点将放在非线性效应最为明显的三维非轴对称梁上。其次，对调制波列的共振自加速进行了理论研究；波列包络与诱导的水平平均流之间的这种强烈的非线性相互作用可能会导致近垂直传播的波列的不稳定和破裂。虽然从日常经验来看不像海洋表面波那样熟悉，但内部重力波实际上在海洋、湖泊和大气中普遍存在，在这些地方它们在传递动量和能量方面发挥着重要作用。特别是内部重力波束经常由雷暴触发，数值模拟和现场观测的证据表明，大气中重力波活动的一个重要组成部分是束状结构。因此，了解内重力波束的传播特性在天气预报中将是有用的。该奖项由数学科学司和工程局共同资助，作为数学科学优先领域的一部分。