Hamiltonian formalism in wave turbulence problems

波湍流问题中的哈密顿形式主义

基本信息

  • 批准号:
    2307712
  • 负责人:
  • 金额:
    $ 22万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2023
  • 资助国家:
    美国
  • 起止时间:
    2023-08-01 至 2026-07-31
  • 项目状态:
    未结题

项目摘要

This project contributes to a better understanding of nonlinear phenomena related to ocean waves. Of special interest are two problems that involve complex interactions between surface waves and underlying currents or between surface waves and floating structures. These coupled processes are still not well understood and raise challenging questions in oceanography and engineering. Wave-current interactions play a key role in many circumstances like the generation of rogue waves or the transport of contaminants in the open ocean, as well as the mechanism of sediment transport which drives beach erosion in coastal areas. All these have far-reaching implications for a broad range of human activities related to the shipping, tourism, fishing or oil industries, and coastal infrastructure. An important application of wave-structure interactions is to wave power extraction by floating wave energy converters. Ocean waves have great potential as a source of renewable energy but entail many scientific challenges. Wave farms where arrays of wave energy converters are placed in a geometric configuration over extended maritime areas have been considered as a serious option. Determination of the optimal configuration under various wave conditions is crucial for maximizing power absorption in such a system. This research develops new mathematical models for these coupled phenomena that have so far been poorly represented in operational wave forecasting yet are of great relevance in the context of climate change and energy crisis. This project also provides opportunities for the participation and training of graduate students.Under consideration are situations where nonlinear wave interactions occur over a wide range of length and time scales in a complex environment, which poses serious difficulties for their asymptotic analysis and numerical simulation. Examples include ocean waves interacting with a vortical current and ocean waves interacting with an array of floating wave energy converters. In both cases, a Hamiltonian formulation can be established to describe the problem and therefore Hamiltonian techniques are ideal to properly analyze it. Such techniques however are still not sufficiently advanced in the context of nonlinear partial differential equations. The investigator constructs building blocks for this Hamiltonian formalism where the presence of multiple scales can be naturally accommodated in the asymptotic analysis while producing approximations that preserve important structural properties such as energy conservation. This research contributes to the development of the theory of weak wave turbulence in complex media. Both deterministic and statistical viewpoints are adopted to obtain reduced nonlinear models for the long-time evolution of the wave amplitude and wave spectrum. Exact equilibrium solutions of these model equations associated with invariants of motion are derived and numerical simulations for more general nonlinear cases are performed to complement the theoretical predictions.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
该项目有助于更好地理解与海浪有关的非线性现象。特别感兴趣的是两个问题,涉及复杂的相互作用之间的表面波和底层电流或表面波和浮动结构。这些耦合过程仍然没有得到很好的理解,并在海洋学和工程提出了具有挑战性的问题。波流相互作用在许多情况下起着关键作用,例如在开阔海洋中产生流氓波或污染物的运输,以及驱动沿海地区海滩侵蚀的沉积物运输机制。所有这些都对与航运、旅游业、渔业或石油工业以及沿海基础设施有关的一系列广泛的人类活动产生了深远的影响。波浪-结构相互作用的一个重要应用是通过浮式波能转换器提取波能。海浪作为可再生能源的巨大潜力,但也带来了许多科学挑战。波浪发电场将波浪能转换器阵列以几何配置放置在广阔的海域上,已被认为是一个重要的选择。在各种波浪条件下确定最佳配置对于最大化这种系统中的功率吸收至关重要。这项研究为这些耦合现象开发了新的数学模型,这些现象迄今为止在业务波浪预报中表现不佳,但在气候变化和能源危机的背景下具有重要意义。本项目还为研究生的参与和培训提供了机会。考虑的情况下,非线性波相互作用发生在一个复杂的环境中,在广泛的长度和时间尺度,这给他们的渐近分析和数值模拟带来了严重的困难。示例包括与涡流相互作用的海浪和与浮动波浪能转换器阵列相互作用的海浪。在这两种情况下,可以建立一个哈密顿公式来描述问题,因此哈密顿技术是理想的,以正确地分析它。然而,这种技术仍然没有足够先进的非线性偏微分方程的上下文中。研究者构建了这种哈密顿形式主义的积木,在这种形式主义中,多个尺度的存在可以自然地容纳在渐近分析中,同时产生近似,保持重要的结构特性,如能量守恒。该研究有助于复杂介质中弱波湍流理论的发展。从确定性和统计性两个角度出发,得到了波浪振幅和波谱长期演化的简化非线性模型。这些模型方程与运动不变量的精确平衡解推导和更一般的非线性情况下进行数值模拟,以补充理论predictions.This奖项反映了NSF的法定使命,并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

项目成果

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Philippe Guyenne其他文献

A Flume Experiment on the Adjustment of the Mean and Turbulent Statistics to a Transition from Short to Tall Sparse Canopies
  • DOI:
    10.1007/s10546-008-9309-7
  • 发表时间:
    2008-09-13
  • 期刊:
  • 影响因子:
    2.200
  • 作者:
    Anthony Seraphin;Philippe Guyenne
  • 通讯作者:
    Philippe Guyenne
A boundary perturbation method to simulate nonlinear deformations of a two-dimensional bubble
模拟二维​​气泡非线性变形的边界摄动方法

Philippe Guyenne的其他文献

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{{ truncateString('Philippe Guyenne', 18)}}的其他基金

Nonlinear Dispersive Water Waves in Multiscale Interaction Problems
多尺度相互作用问题中的非线性色散水波
  • 批准号:
    1615480
  • 财政年份:
    2016
  • 资助金额:
    $ 22万
  • 项目类别:
    Standard Grant

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