CMG COLLABORATIVE RESEARCH: A Systematic Approach to Large Amplitude Internal Wave Dynamics: An Integrated Mathematical, Observational, and Remote Sensing Model

该研究将开发一种有效且准确的理论模型来研究可变底部地形上大幅度内孤立波的产生、传播和转换，然后将所得内波模型与改进的雷达成像模型相结合，以遥感这些强非线性内波的表面特征。在应用数学家和物理海洋学家之间的密切合作下，模型预测将通过从最近/正在进行/未来的现场活动和卫星雷达图像收集的现场数据进行验证。将实现欧拉方程的高精度数值积分，并将为一系列原型测试用例提供内波模型的进一步交叉验证。具体来说，本研究活动将：（1）推广和改进新推导的第一原理模型，以描述在近似连续密度分层的多层系统中传播的二维内波； （2）用几个关键物理过程的欧拉方程的完全非线性数值解来验证模型； (3) 在现有的实验室实验和二维纳维-斯托克斯方程的新直接数值模拟的指导下，结合内波破碎和底部摩擦能量耗散的新参数化； (4) 结合表面特征和雷达后向散射模型的耦合，并将其与南海雷达数据进行比较； (5)利用南海三组现场实验数据(ASIAEX、WISE/VANS、NLIWI)为模型验证奠定基础，重点关注内孤立波的发生和演化。这个高度跨学科的项目将为预测和监测海洋内波活动提供全面但实用的工具。由于仪器技术的进步，海洋动力学的这一组成部分最近变得更容易直接观测。随着这些进展，现在我们可以认识到极端事件，例如亚洲海国际声学实验（ASIAEX）在南海观测到的振幅高达140 m的大型内波，经常发生并携带巨大的能量，除其他外，可能导致强流的产生以及随之而来的热量和其他海洋示踪剂的混合和分布。随着人类活动的扩展以及越来越多地受到和影响地球耦合海洋和大气系统的演化，对地球耦合海洋和大气系统的这些动力学特征的准确预测变得越来越重要。该领域未来研究人员的教育需要数学和地球物理应用之间的进一步复杂化和信息流动。拟议研究的更广泛影响将包括对博士后、研究生和本科生进行培训并融入他们的研究计划，并与该提案的建模和实验 PI 密切联系。除了通过期刊出版物和参加会议和研讨会的传统传播渠道之外，我们的研究结果和成果还将通过专门的网站向科学界公布。

The proposed research will develop an effective and accurate theoretical model to investigate the generation, propagation, and transformation of large amplitude internal solitary waves over variable bottom topography, and then integrate the resulting internal wave model with an improved radar imaging model for remote sensing of the surface signatures of these strongly nonlinear internal waves. In close collaboration between applied mathematicians and physical oceanographers, model predictions will be validated with in-situ data collected from recent/on-going/future field campaigns and satellite radar images. High accuracy numerical integration of the Euler equations will be implemented and will offer further cross verification of the internal wave model for a series of prototypical test cases. Specifically, this research activity will: (1) generalize and improve newly derived first principle models to describe two-dimensional internal waves propagating in a multi-layer system approximating continuous density stratification; (2) verify the models with fully nonlinear numerical solutions of the Euler equations for several crucial physical processes; (3) incorporate new parameterizations of energy dissipation by internal wave breaking and bottom friction, guided by available laboratory experiments and new direct numerical simulations of the two-dimensional Navier-Stokes equations; (4) incorporate coupling with models for surface signatures and radar backscatter, and compare these with South China Sea radar data; and (5) set the basis for the validation of the models with three sets of field experimental data (ASIAEX, WISE/VANS, NLIWI) in the South China Sea focusing on genesis and evolution of internal solitary waves. This highly interdisciplinary project will provide a comprehensive but practical tool for predicting and monitoring internal wave activity in the ocean. Such a component of ocean dynamics has recently become more accessible to direct observation thanks to technological improvements in instrumentation. With these advances, it is now possible to appreciate that extreme events, such as the large internal waves with amplitudes of up to 140 m observed in the South China Sea by the Asian Seas International Acoustics Experiment (ASIAEX), occur frequently and carry tremendous energy which can result in, among other things, the generation of strong currents and ensuing mixing and distribution of heat and other ocean tracers. Accurate prediction of these dynamical features of the earth coupled ocean and atmosphere system is becoming more and more important as human activity expands and is increasingly affected by, and affects, the evolution of this system. The education of future researchers in this area requires further sophistication and flow of information between the mathematical and geophysical application. The broader impact of the research proposed will include training and integration into the research program of postdoctoral, graduate, and undergraduate students, in close contact with both the modeling and the experimental PIs of the proposal. Our findings and results will be made available to the scientific community through a dedicated website, besides the classical channels of dissemination through journal publications and participation to conferences and seminars.