Theoretical Studies in Fluid Dynamics and Geophysical Fluid Dynamics

大气和海洋现象的组织性和复杂性极其丰富;其中许多现象无法通过实验产生。 这些现象涉及广泛的时间和空间尺度。 对这些复杂现象和相关科学问题的理解是当代科学的重大挑战之一，并具有巨大的社会影响。 研究人员建议研究流体动力学和地球物理流体动力学的性质和理论，重点是流体流动和地球物理流体流动的结构，其形成，其鲁棒性/稳定性和过渡。 该研究围绕低频气候变率的新策略，特别包括三个相互关联领域的特定主题：（A）动态分叉理论及其在流体力学中的应用，（B）地球物理流体动力学中的分叉和稳定性问题，和（C）不可压缩流体流动和地球物理流体流动的几何理论。研究重点是基本流体动力学问题和地球物理流体动力学问题，包括温盐环流和与厄尔尼诺预测相关的热带环流。 研究人员使用物理建模，严格的数学理论和大规模计算的组合来产生对物理现象的新见解。 所提出的研究涉及一方面现有的数学理论的应用，以了解潜在的物理问题，另一方面新的数学理论的发展。 特别是，拟议的工作是基于两个新的数学理论，这是最近开发的PI与天马合作。 这些理论是由地球物理流体动力学的研究所激发的，并对科学和工程中的其他学科有额外的益处。 拟议的项目涉及具有挑战性的问题，具有重要的实际意义的地球物理工作量化的可预测性，分析误差增长的动力学模型，并制定有效的预测方法。 这些调查将大大有助于改善对天气和气候变化的预测，这对我们的经济至关重要。

The phenomena of the atmosphere and ocean are extremely rich in their organization and complexity; many of them cannot be produced by experiments. These phenomena involve a broad range of temporal and spatial scales. The understanding of these complicated phenomena and the relevant scientific issues is one of the grand challenges of contemporary science, and has huge societal impacts. The investigator proposes to study the nature and theory of fluid dynamics and geophysical fluid dynamics, focusing on the structure, its formation, its robustness/stability and transitions of fluid flows and geophysical fluid flows. The study is centered around novel strategies for low-frequency climate variabilities, including in particular specific topics in three interrelated areas: (A) dynamic bifurcation theory and its applications to fluid mechanics,(B) bifurcation and stability issues in geophysical fluid dynamics, and(C) a geometrical theory of incompressible fluid flows and geophysical fluid flows.The study focuses on both fundamental fluid dynamics problems and geophysical fluid dynamics problems including the thermohaline circulation and the tropical circulations associated with the El Nino prediction. The investigator uses a combination of physical modeling, rigorous mathematical theory, and large-scale computing to yield new insights into physical phenomena. The proposed study involves on the one hand applications of existing mathematical theory to the understanding of the underlying physical problems, and on the other hand the development of new mathematical theories. In particular, the proposed work is based on two new mathematical theories which are developed recently by the PI in collaboration with Tian Ma. These theories are motivated by the study in geophysical fluid dynamics, and have additional benefit for other disciplines in science and engineering. The proposed project involves challenging problems with important practical implications for geophysical efforts to quantify predictability, analyze error growth in dynamical models, and develop efficient forecast methods. These investigations will be of great benefit in improving predictions on weather and climate changes, which are of central importance to our economy.