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

基本信息

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

项目摘要

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，其中温度和盐度随深度而变化。特别是，已知非线性共振相互作用在表面波谱和内波谱的长期演化中发挥着至关重要的作用。此外，最近的遥感观测表明，内波可以显着改变海洋表面的表现。因此，更好地理解非线性表面波和内波的动力学及其相互作用对于物理海洋学、环境科学以及海洋和海岸工程等许多学科至关重要。最终，这些信息将有助于研究气候变化的研究人员，因为跨越海空边界和海洋内部的能量和动量转移是他们工作的基础。该项目将通过新泽西理工学院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参与研究提供机会。该项目将对最近开发的两层流中多向波的显式哈密顿系统进行数值研究，并将推导之间的近共振相互作用的简化模型窄带二维表面波和大幅度长内波。考虑到现实的海洋条件，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以及随后两种波模式之间的能量传递的影响。重点是满足所谓群共振条件的短表面波包的演化，这要求包的群速度与长内波的相速度大致匹配。在现实的海洋条件下，这个条件很容易满足。然后，将使用通过非定常共形映射技术和之前的实验室观察获得的欧拉方程的完全非线性数值解来验证一维波的数学模型。两层流的理论方法将扩展到三层流，并且将研究前两种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之外，还将研究无能量交换的特殊共振相互作用，以找到行波和稳态解决方案。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值进行评估，被认为值得支持以及更广泛的影响审查标准。