CMG COLLABORATIVE RESEARCH: From internal waves to mixing in the ocean

采用数学波浪平均相互作用理论、物理模型、数值模拟和与观测场数据的比较相结合的多管齐下的方法，研究了内波对海洋示踪剂输运速率的贡献。将研究的具体课题包括由破裂的内波引起的示踪剂的垂直和水平混合，由不间断的内波引起的示踪剂的水平弥散，以及由地转气流在地形上产生的波引起的结构和传输。提出的研究是及时和积极的，首先是因为高分辨率海洋数据的当前和日益增加，其次是因为目前开始了一个允许重力波的海洋模型时代。在这样的模型中，我们可以预计在未来几年中会出现数值重力波，尽管是在模型分辨率的门槛。这项研究预计将提供更好的指导和改进的框架，以便在实地和高分辨率数值模式中解释次中尺度观测。研究这些问题也提出了新的数学研究问题，例如在非高斯波理论领域。因此，该项目是相互交织的数学和地球物理研究轨迹之间的概念双向联系。广泛影响这一理论研究的结果可能会为未来设计下一代海洋天气和气候预报系统提供参考，这具有重要的社会意义。在教育方面，高等数学和应用科学方面的培训对这项建议的研究内容至关重要。该提案包括培训一名博士后研究员和一名博士生，并为对研究经验感兴趣的高级本科生提供基于功绩的津贴。经验表明，这种对根本重要课题的早期研究经验可以促使本科生决定申请数学或其他自然科学专业的研究生院。

The contribution of internal waves to the rate of tracer transport in the ocean is investigated using a multi-pronged approach that combines mathematical wave?mean interaction theory, physical modeling, numerical simulation, and comparison with observational field data. Specific topics to be studied include the vertical and horizontal mixing of tracers induced by breaking internal waves, the horizontal dispersion of tracers by non-breaking internal waves, and the structure and transport induced by waves generated by geostrophic flow over topography.Intellectual meritThe proposed research is timely and motivated firstly because of the current and increasing availability of high-resolution ocean data, and secondly because of the current dawning of an era of gravity-wave-permitting ocean models. In such models we can anticipate in the coming years the emergence of numerical gravity waves, albeit at the threshold of the model resolution. This research is anticipated to provide better guidance and an improved framework in which to interpret sub-mesoscale observations both in the field and in high-resolution numerical models. Investigating these issues also raises new mathematical research questions, for instance in the area of non-Gaussian wave theory. So this project is a conceptual two-way link between intertwining mathematical and geophysical research trajectories.Broader impactResults from this theoretical study may feed into the future design of next-generation ocean forecasting systems for weather and climate, which is of great societal importance. On the educational side, training in advanced mathematics and applied science is paramount to the research elements of this proposal. The proposal includes training of a post-doctoral researcher and a PhD student as well as provision for merit-based stipends for advanced undergraduates interested in research experiences. Experience shows that such early research experiences on topics of fundamental importance can trigger an undergraduate's decision to apply for graduate school in mathematics or in another natural science.