CMG: Nonintegrable Hamiltonian Systems in Ocean Dynamics

CMG:海洋动力学中的不可积哈密顿系统

基本信息

  • 批准号:
    0417425
  • 负责人:
  • 金额:
    $ 96.4万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Continuing Grant
  • 财政年份:
    2004
  • 资助国家:
    美国
  • 起止时间:
    2004-09-01 至 2009-08-31
  • 项目状态:
    已结题

项目摘要

Abstract: 0417425CMG: Nonintegrable Hamiltonian Systems in Ocean DynamicsThis study focuses on two sets of problems in ocean physics in which the underlying dynamics are those of a nonintegrable Hamiltonian system: (i) particle trajectory (Lagrangian) dynamics in unsteady two-dimensional incompressible flows; and (ii) wave propagation in inhomogeneous moving media. The issues to be investigated in both cases are motivated by oceanographic questions rather than purely mathematical issues. However, it is anticipated that greater attention to mathematical detail than has heretofore been applied will lead to new insights into some very practical issues.Intellectual Merit. Traditional approaches to the above two classes of problem rely heavily on strictly stochastic methods. From a dynamical systems perspective such an approach is unrealistic and unnecessarily restrictive. Topics relating to problem (i) to be investigated include: stochastic vs. chaotic dynamics; tracer patchiness and anomalous diffusion; the importance of the background flow on trajectory stability; the importance of vorticity constraints on trajectory stability; adiabatic invariance; and a detailed investigation of mixing in perturbed Taylor-Couette flows. Of particular concern in problem (ii) is the development of a theory of wave propagation in random inhomogeneous media (WPRIM); preliminary work on this problem suggests that it differs in some fundamental respects from the traditional (homogeneous background) WPRM problem. Broader Impacts. The proposed work is a collaboration between geoscientists and a mathematician. It will serve to launch the careers of two promising, young scientists who are members of underrepresented groups. The collaboration between the geoscientists and mathematicians will improve the level of mathematical rigorof the geophysically motivated research performed and develop geophysically motivated teaching material for use in mathematics courses. The latter is particularly important at the undergraduate level to point out the practical importance of the material being taught. Web-based teaching aids will be developed. The proposed activity offers several possibilities to further the education of graduate students; at least one will be involved in the proposed work. The proposed work also has numerous practical applications that are beneficial to society. The principal application of the Lagrangian dynamics work is to mixing (e.g. pollutant dispersal) in the atmosphere, the ocean, or other natural bodies of water. The issue of Lagrangian predictability is relevant to pollutant dispersal issues and search and rescue operations at sea. Understanding tracer concentration statistics, including tracer patchiness, can be critically important in biological applications. The proposed work relating to mixing in Taylor-Couette flows has immediate industrial applications, for example to the mixing of chemicals or drugs; in the latter case, failure to thoroughly mix could lead to a localized concentration of a substance that is toxic to humans. The principal application of the WPRIM work is to inverse problems (tomography, nondestructive evaluation) and communication. Waves (acoustics, elastic, electromagnetic) are widely used in geophysical applications of both types. The environment in almost all such geophysical applications is characterized by an inhomogeneous background; hence the importance of the proposed work for understanding wavefield statistics and loss of signal coherence.
摘要:海洋动力学中的不可积哈密顿系统本文研究了海洋物理学中两组以不可积哈密顿系统为基础的动力学问题:(i)非定常二维不可压缩流中的粒子轨迹(拉格朗日)动力学;(2)波在非均匀运动介质中的传播。在这两种情况下要调查的问题都是由海洋学问题而不是纯粹的数学问题引起的。然而,预计对数学细节的更多关注将比以往应用将导致对一些非常实际的问题的新见解。知识价值。解决上述两类问题的传统方法严重依赖于严格的随机方法。从动态系统的角度来看,这种方法是不现实的,而且是不必要的限制。与问题(i)相关的主题将被研究包括:随机与混沌动力学;示踪剂斑块和异常扩散;背景流对弹道稳定性的重要性;涡度约束对弹道稳定性的重要性;绝热不变性;以及对扰动泰勒-库埃特流混合的详细研究。在问题(ii)中特别值得关注的是随机非均匀介质中波传播理论(WPRIM)的发展;对这个问题的初步研究表明,它在一些基本方面不同于传统的(同质背景)WPRM问题。更广泛的影响。这项提议的工作是地球科学家和数学家之间的合作。它将为两名有前途的年轻科学家的职业生涯提供帮助,他们是代表性不足的群体的成员。地球科学家和数学家之间的合作将提高以地球物理为动机的研究的数学严谨性水平,并开发以地球物理为动机的教材用于数学课程。后者在本科阶段特别重要,它指出了所教授材料的实际重要性。开发网络教学辅助工具。提议的活动为研究生的进一步教育提供了几种可能性;至少有一个人将参与拟议的工作。所提出的工作也有许多对社会有益的实际应用。拉格朗日动力学功的主要应用是大气、海洋或其他自然水体中的混合(例如污染物扩散)。拉格朗日可预测性问题与污染物扩散问题和海上搜救行动有关。了解示踪剂浓度统计,包括示踪剂斑块,在生物学应用中是至关重要的。与泰勒-库埃特流混合有关的拟议工作具有直接的工业应用,例如化学品或药物的混合;在后一种情况下,未能完全混合可能导致局部浓度的物质对人体有毒。WPRIM工作的主要应用是逆问题(层析成像、无损评估)和通信。声波(声学、弹性、电磁)在这两种类型的地球物理应用中都得到了广泛的应用。几乎所有这类地球物理应用的环境都具有不均匀背景的特点;因此,所提出的工作对于理解波场统计和信号相干损失的重要性。

项目成果

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Francisco Beron-Vera其他文献

Francisco Beron-Vera的其他文献

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{{ truncateString('Francisco Beron-Vera', 18)}}的其他基金

Collaborative Research: Enhancing our Understanding of North Atlantic Deep Water Pathways using Nonlinear Dynamics Techniques
合作研究:利用非线性动力学技术增强我们对北大西洋深水路径的理解
  • 批准号:
    1851097
  • 财政年份:
    2019
  • 资助金额:
    $ 96.4万
  • 项目类别:
    Standard Grant
Workshop: Coherent Structures in Dynamical Systems; Lorentz Center, Leiden, The Netherlands; 16-20 May 2011
研讨会:动力系统中的相干结构;
  • 批准号:
    1057412
  • 财政年份:
    2010
  • 资助金额:
    $ 96.4万
  • 项目类别:
    Standard Grant
Collaboration in Mathematical Geosciences: Nonintegrable Hamiltonian Systems in Geophysical Fluid Dynamics
数学地球科学合作:地球物理流体动力学中的不可积哈密顿系统
  • 批准号:
    0825547
  • 财政年份:
    2008
  • 资助金额:
    $ 96.4万
  • 项目类别:
    Standard Grant

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Collaboration in Mathematical Geosciences: Nonintegrable Hamiltonian Systems in Geophysical Fluid Dynamics
数学地球科学合作:地球物理流体动力学中的不可积哈密顿系统
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    0825547
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    2008
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    $ 96.4万
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    Standard Grant
Topology of nonintegrable plane fields
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  • 批准号:
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Nonintegrable Phases and Nonlocality in Physics
物理学中的不可积相和非定域性
  • 批准号:
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  • 财政年份:
    1988
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    $ 96.4万
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Mathematical Sciences: Singularities of Integrable and Nonintegrable Dynamic Systems
数学科学:可积和不可积动态系统的奇异性
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  • 财政年份:
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