Nonlinear Resonant Wave Interactions in Density-Stratified Flows

密度分层流中的非线性共振波相互作用

• 批准号: 2108524
• 负责人: Wooyoung Choi
• 金额: $ 36万
• 依托单位: New Jersey Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-09-01 至 2025-05-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2108524&HistoricalAwards=false
• 关键词: Nonlinear; Resonant; Wave; Interactions; Density

Nonlinear internal waves and their interaction with surface waves have been frequently observed in density-stratified oceans, where the temperature and salinity vary with depth. In particular, nonlinear resonant interactions have been known to play a crucial role in the long-term evolution of surface and internal wave spectra. In addition, recent observations from remote sensing have shown that internal waves can substantially change the surface expression of the ocean. Therefore, a better understanding of the dynamics of nonlinear surface and internal waves and their interactions is crucial in many disciplines, including physical oceanography, environmental science, and ocean and coastal engineering. Ultimately this information would help researchers working on climate change as the transfer of energy and momentum across the air-sea boundary and in the interior of the ocean is fundamental to their work. This project will address several aspects of the dynamical interaction of internal and surface waves through a combination of modeling, numerical simulations, and experiments at the newly developed wave research laboratory at NJIT. The project will also provide opportunities for the involvement of undergraduate and graduate students in the research.This project will study numerically the recently developed explicit Hamiltonian system for multi-directional waves in two-layered flows and will derive reduced models for near-resonant interactions between narrow-banded 2D surface waves and a large amplitude long internal wave. With keeping realistic oceanic conditions in mind, the project will study the effects of wave direction, bandwidth, and high-order nonlinearity on the modulation of surface waves induced by internal waves and the subsequent energy transfer between the two wave modes. The focus is on the evolution of a packet of short surface waves satisfying the so-called group resonance condition, which requires the group velocity of the packet to match approximately the phase speed of a long internal wave. This condition can be easily met under realistic oceanic conditions. The mathematical models will be then validated for one dimensional waves with fully nonlinear numerical solutions of the Euler equations obtained via an unsteady conformal mapping technique and previous laboratory observations. The theoretical approach for two-layered flows will be extended to three-layered flows, and the conditions for resonant interactions between the first two internal wave modes and their dynamics will be studied. In addition to time-periodic resonant interactions, a special resonant interaction with no energy exchange will be examined to find traveling wave and steady-state solutions.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.

在温度和盐度随深度变化的密度分层海洋中，经常观察到非线性内波及其与表面波的相互作用。特别是，非线性共振相互作用已被称为在表面和内部波谱的长期演变中发挥至关重要的作用。此外，最近的遥感观测表明，内波可以大大改变海洋的表面表达。因此，更好地了解非线性表面波和内波的动力学及其相互作用在许多学科中是至关重要的，包括物理海洋学，环境科学，海洋和海岸工程。最终，这些信息将有助于研究气候变化的研究人员，因为跨越海气边界和海洋内部的能量和动量转移对他们的工作至关重要。该项目将通过NJIT新开发的波浪研究实验室的建模，数值模拟和实验相结合，解决内波和表面波动态相互作用的几个方面。该项目还将为本科生和研究生提供参与研究的机会。该项目将对最近开发的双层流中多向波的显式哈密顿系统进行数值研究，并将推导窄带二维表面波和大振幅长内波之间近共振相互作用的简化模型。考虑到实际的海洋条件，该项目将研究波浪方向、带宽和高阶非线性对内波引起的表面波调制的影响以及随后两种波模式之间的能量转移。重点是在一个包的短表面波满足所谓的群共振条件，这需要的包的群速度，以匹配大约一个长的内波的相速度的演变。这个条件在实际的海洋条件下很容易满足。然后，将通过非定常保角映射技术和先前的实验室观测结果，利用欧拉方程的完全非线性数值解，对一维波浪的数学模型进行验证。两层流动的理论方法将扩展到三层流动，并将研究前两个内波模式之间的共振相互作用的条件及其动力学。除了时间周期共振相互作用，一个特殊的共振相互作用，没有能量交换将被检查，以找到行波和稳态的解决方案。这个奖项反映了NSF的法定使命，并已被认为是值得通过评估使用基金会的智力价值和更广泛的影响审查标准的支持。

项目成果

High-order strongly nonlinear long wave approximation and solitary wave solution

• DOI: 10.1017/jfm.2022.544
• 发表时间: 2022-07
• 期刊: Journal of Fluid Mechanics
• 影响因子: 3.7
• 作者: W. Choi

Parasitic Capillary Waves on Small-Amplitude Gravity Waves with a Linear Shear Current

具有线性剪切流的小振幅重力波上的寄生毛细波

• DOI: 10.3390/jmse9111217
• 发表时间: 2021
• 期刊: Journal of Marine Science and Engineering
• 影响因子: 2.9
• 作者: Murashige, Sunao;Choi, Wooyoung
• 通讯作者: Choi, Wooyoung

Two-dimensional stability analysis of finite-amplitude interfacial gravity waves in a two-layer fluid

两层流体中有限振幅界面重力波的二维稳定性分析

• DOI: 10.1017/jfm.2022.145
• 发表时间: 2022
• 期刊: Journal of Fluid Mechanics
• 影响因子: 3.7
• 作者: Murashige, Sunao;Choi, Wooyoung
• 通讯作者: Choi, Wooyoung

High-order strongly nonlinear long wave approximation and solitary wave solution. Part 2. Internal waves

• DOI: 10.1017/jfm.2022.950
• 发表时间: 2022-12
• 期刊: Journal of Fluid Mechanics
• 影响因子: 3.7
• 作者: W. Choi