Theoretical Studies in Geophysical Fluid Dynamics

研究者建议研究大尺度大气和海洋环流的结构、稳健性/稳定性和转变，以便更好地了解大气和海洋环流低频变率的典型来源的预测和可预测性。拟议的努力研究两个相互关联领域的具体主题：A)不可压缩和地球物理流体流动的几何理论，以及B)大气和海洋流动的低频变率。第一个领域的拟议工作侧重于底层物理空间中不可压缩和地球物理流体流动的结构转变。第二个领域的工作重点是研究环流尺度海洋环流的分岔问题。研究者将物理建模、严格的数学理论和大规模计算相结合，以产生对物理现象的新见解。所提出的研究一方面涉及应用现有的数学理论来理解潜在的物理问题，另一方面涉及发展新的数学理论。拟议的项目涉及具有重要实际意义的具有挑战性的问题，对地球物理量化可预测性，分析动力学模型中的误差增长以及开发有效的预测方法具有重要的实际意义。这些调查将对改善天气和气候变化的预测有很大的好处，这对我们的经济至关重要。

The investigator proposes to study the structure, its robustness/stability and transitions of the large scale atmospheric and oceanic flows, to yield a better understanding of the atmospheric and oceanic prediction and predictability relevant to typical sources of their low frequency variability. The proposed effort studies specific topics in two inter-related areas: A) geometric theory of incompressible and geophysical fluid flows, and B) low-frequency variability of atmospheric and oceanic flows. The proposed work in the first area focuses on the structural transitions of incompressible and geophysical fluid flows in the underlying physical spaces. The proposed work in the second area focuses on bifurcation issues of gyre scale ocean circulations. The investigator uses a combination of physical modelling, rigorous mathematical theory, and large scale computing to yield new insights into physical phenomena. The proposed study involves on the one hand applications of the existing mathematical theory to the understanding of the underlying physical problems, and on the other hand the development of new mathematical theories. 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.