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

这项研究将建立一个有效和准确的理论模型来研究在可变海底地形上大幅度内孤立波的产生、传播和转换，然后将所得到的内波模型与改进的雷达成像模型相结合，用于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，将利用从最近/正在进行/未来的实地活动和卫星雷达图像收集的现场数据来验证模型预测。将对欧拉方程进行高精度的数值积分，并将为一系列原型测试案例提供对内波模型的进一步交叉验证。具体地说，这项研究工作将：(1)推广和改进新导出的描述二维内波在近似连续密度层化的多层系统中传播的第一原理模型；(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新的二维N-S方程的直接数值模拟的指导下，加入新的内波破碎和底摩擦能量耗散的参数化；(4)结合表面特征和雷达后向散射模型的耦合，并将其与南海中国雷达资料进行比较；(5)以南中国海区内孤立波的成因和演化为基础，利用ASIAEX、WISE/VANS、NLIWI三组海面试验资料对模型进行了验证。这个高度跨学科的项目将为预测和监测海洋中的内波活动提供一个全面而实用的工具。由于仪器技术的改进，海洋动力学的这一组成部分最近变得更容易进行直接观测。随着这些进展，现在可以认识到，极端事件，例如亚洲海洋国际声学实验在南中国海观测到的振幅高达140m的大内波，频繁发生并携带巨大能量，除其他外，可能导致强流的产生以及随后热量和其他海洋示踪物的混合和分配。随着人类活动的扩展，对地球-海洋-大气耦合系统的这些动力学特征的准确预测变得越来越重要，并且越来越多地受到该系统的影响和影响。未来研究人员在这一领域的教育需要进一步完善数学和地球物理应用之间的信息流动。拟议研究的更广泛影响将包括培训和融入博士后、研究生和本科生的研究计划，与提案的建模和实验PI密切联系。我们的调查结果和结果将通过一个专门的网站向科学界公布，除了通过期刊出版物和参加会议和研讨会的传统渠道。

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.