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.

非线性内波及其与表面波的相互作用经常在密度分层的海洋中观察到，其中温度和盐度随着深度而变化。特别是，已知非线性谐振相互作用在表面和内波光谱的长期演变中起着至关重要的作用。此外，遥感的最新观察结果表明，内部波可以大大改变海洋的表面表达。因此，在许多学科中，对非线性表面和内部波的动态及其相互作用的更好理解在包括物理海洋学，环境科学以及海洋和沿海工程中至关重要。最终，这些信息将帮助研究人员从事气候变化的研究，因为能源和动力在整个空气海边界上的转移以及海洋内部的转移至关重要。该项目将通过建模，数值模拟以及NJIT新开发的波浪研究实验室的实验的组合来解决内部和表面波的动态相互作用的几个方面。该项目还将为研究生参与研究提供机会。该项目将在数值上研究最近开发的两层流量中的明显的汉密尔顿系统，用于多个流量的多向波，并将得出缩小模型，以减少近谐波相互作用的模型，以在狭窄的2D表面波和大型振幅内部浪潮之间进行近谐声相互作用。考虑到逼真的海洋条件，该项目将研究波动方向，带宽和高阶非线性对由内波引起的表面波的调节以及两种波模式之间的随后能量传递的影响。重点是满足所谓的组共振条件的一包短表面波的演变，这需要数据包的组速度匹配长度内波的相位速度。在逼真的海洋条件下，可以很容易地满足这种情况。然后，将使用通过不稳定的共形映射技术和以前的实验室观察结果获得的EULER方程的完全非线性数值解的一维波验证数学模型。两层流的理论方法将扩展到三层流，并且将研究前两个内部波模式及其动力学之间的共振相互作用的条件。除了时间周期性的谐振相互作用外，还将检查没有能量交换的特殊谐振互动，以找到波动波和稳态解决方案。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛影响的评估标准通过评估来获得支持的。

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