Three-Dimensional Nonlinear Internal Wave Beams: Mathematical Models and Laboratory Experiments

三维非线性内波梁:数学模型和实验室实验

基本信息

项目摘要

Density-stratified fluids support internal gravity waves due to the restoring force of buoyancy. Although not as familiar as free-surface waves, internal waves in fact are ubiquitous in oceans, lakes, and the atmosphere. In these natural settings, stratification is caused by temperature variations as well as changes in salinity (in oceans) and pressure (in the atmosphere). Internal wave motion is inherently anisotropic because gravity provides a preferred direction. As a result, energy is transported in the form of wave beams, which are the analogues of the familiar circular wave fronts in isotropic media. Internal wave beams are of great geophysical interest because they form the backbone of the oceanic internal tide; moreover, in the atmosphere, they frequently arise due to thunderstorms. In contrast to most prior studies, which assume strictly two-dimensional disturbances, this project is concerned with internal wave beams featuring three-dimensional variations, as expected in the field. Motivation comes from recent findings, by the investigator's group and others, that suggest that the propagation of internal wave beams in three dimensions differs fundamentally from its two-dimensional counterpart. Apart from making basic contributions to applied mathematics, this project is expected to also shed light on the role of the oceanic internal tide in momentum deposition, material transport, and deep-ocean mixing. These processes affect climate dynamics, pollutant dispersal, and nutrient cycles. A graduate student is included in the project.This research effort advances theoretical modeling to gain a fundamental understanding of three-dimensional nonlinear internal wave beams, particularly the attendant resonant nonlinear interaction with induced mean flows that is central to three-dimensional wave beam dynamics. Using asymptotic methods, nonlinear evolution equations are derived for three-dimensional beam propagation under conditions of geophysical interest, taking into account the effects of forcing, non-uniform background, dissipation, and the Earth's rotation. These new mathematical models are analyzed by analytical and numerical means in order to understand beam-mean-flow nonlinear interactions from a mathematical and a physical perspective. The theoretical study is supported by companion laboratory experiments that exploit recent advances in three-dimensional flow visualization.
密度分层流体由于浮力的恢复力而支持内部重力波。 内波虽然不像自由表面波那样为人所熟悉,但事实上,内波在海洋、湖泊和大气中无处不在。 在这些自然环境中,分层是由温度变化以及盐度(海洋)和压力(大气)的变化引起的。 内波运动本质上是各向异性的,因为重力提供了优选方向。 因此,能量以波束的形式传输,波束类似于各向同性介质中常见的圆形波前。 内波束具有很大的地球物理意义,因为它们形成了海洋内潮的主干;此外,在大气中,它们经常由于雷暴而出现。 与大多数先前的研究相反,这些研究假设严格的二维扰动,该项目关注的是具有三维变化的内部波束,正如该领域所预期的那样。 动机来自于最近的研究结果,由研究人员的小组和其他人,这表明,内部光束在三维中的传播从根本上不同于其二维对应。 除了对应用数学做出基本贡献外,该项目还有望揭示海洋内潮在动量沉积、物质输送和深海混合中的作用。 这些过程影响气候动态、污染物扩散和养分循环。 该研究工作推进了理论建模,以获得对三维非线性内波束的基本理解,特别是伴随的共振非线性相互作用与诱导平均流,这是三维波束动力学的核心。 使用渐近方法,非线性演化方程推导出三维光束传输的地球物理感兴趣的条件下,考虑到强迫,非均匀背景,耗散和地球自转的影响。 这些新的数学模型进行了分析,以了解从数学和物理的角度束平均流的非线性相互作用的分析和数值方法。 理论研究的支持下,同伴实验室实验,利用三维流动可视化的最新进展。

项目成果

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Triantaphyllos Akylas其他文献

Triantaphyllos Akylas的其他文献

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{{ truncateString('Triantaphyllos Akylas', 18)}}的其他基金

Nonlinear Analysis of Three-Dimensional Water-Wave Patterns via Exponential Asymptotics
通过指数渐近法对三维水波模式进行非线性分析
  • 批准号:
    2004589
  • 财政年份:
    2020
  • 资助金额:
    $ 41.01万
  • 项目类别:
    Standard Grant
Dynamics of Nonlinear Internal Wave Beams in Stratified Flows
层流中非线性内波束的动力学
  • 批准号:
    1107335
  • 财政年份:
    2011
  • 资助金额:
    $ 41.01万
  • 项目类别:
    Standard Grant
Nonlinear Wave Propagation in Fluid Flows
流体中的非线性波传播
  • 批准号:
    0908122
  • 财政年份:
    2009
  • 资助金额:
    $ 41.01万
  • 项目类别:
    Standard Grant
Nonlinear Wave Dynamics in Fluid Flows
流体流动中的非线性波动力学
  • 批准号:
    0604416
  • 财政年份:
    2006
  • 资助金额:
    $ 41.01万
  • 项目类别:
    Continuing Grant
Nonlinear Wave Dynamics in Stratified Flows
层流中的非线性波动力学
  • 批准号:
    0305940
  • 财政年份:
    2003
  • 资助金额:
    $ 41.01万
  • 项目类别:
    Standard Grant
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
  • 财政年份:
    2000
  • 资助金额:
    $ 41.01万
  • 项目类别:
    Standard Grant
Mathematical Sciences: Nonlinear Coupling of Long Internal Waves with Small-Scale Disturbances
数学科学:长内波与小尺度扰动的非线性耦合
  • 批准号:
    9701967
  • 财政年份:
    1997
  • 资助金额:
    $ 41.01万
  • 项目类别:
    Continuing Grant
U.S.-France Cooperative Research: Assymmetric Nonlinear Waves in Fluid Flows
美法合作研究:流体流动中的非对称非线性波
  • 批准号:
    9512852
  • 财政年份:
    1996
  • 资助金额:
    $ 41.01万
  • 项目类别:
    Standard Grant
Mathematical Sciences: Nonlinear Coupling of Long Internal Waves With Small-Scale Disturbances
数学科学:长内波与小尺度扰动的非线性耦合
  • 批准号:
    9404673
  • 财政年份:
    1994
  • 资助金额:
    $ 41.01万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Nonlinear Coupling of Solitary Internal Waves With Small- Scale Disturbances
数学科学:孤立内波与小尺度扰动的非线性耦合
  • 批准号:
    9202064
  • 财政年份:
    1992
  • 资助金额:
    $ 41.01万
  • 项目类别:
    Continuing Grant

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Three-dimensional Nonlinear Structured Illumination for Live Imaging with 80 nm resolution
用于 80 nm 分辨率实时成像的三维非线性结构照明
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    10637540
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Nonlinear Analysis of Three-Dimensional Water-Wave Patterns via Exponential Asymptotics
通过指数渐近法对三维水波模式进行非线性分析
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A three-dimensional study of nonlinear wave propagation in brass instruments
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