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

内波的示踪剂在海洋中的传输率的贡献进行了研究，使用多管齐下的方法，结合数学波？平均相互作用理论、物理模拟、数值模拟以及与观测资料的比较。具体的研究课题包括破碎内波引起的示踪剂的垂直和水平混合、非破碎内波引起的示踪剂的水平扩散以及地形上地转流产生的波浪引起的结构和输运。智力价值拟议的研究是及时和有动力的，首先是因为目前和越来越多的高分辨率海洋数据，其次是因为目前重力波允许的海洋模型时代的曙光。在这样的模型中，我们可以预测在未来几年中出现的数值重力波，虽然在模型分辨率的阈值。这项研究预计将提供更好的指导和改进的框架，在其中解释亚中尺度观测在外地和高分辨率数值模式。调查这些问题也提出了新的数学研究问题，例如在非高斯波动理论领域。因此，这个项目是一个概念上的双向联系交织的数学和地球物理研究trajectors.broader影响从这个理论研究的结果可能会馈入未来的设计下一代海洋天气和气候预报系统，这是非常重要的社会。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，以及为对研究经验感兴趣的高年级本科生提供基于成绩的津贴。经验表明，这种早期的研究经验，对根本的重要性的主题可以触发本科生的决定，申请研究生院在数学或其他自然科学。

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.