Theoretical Studies in Geophysical Fluid Dynamics

研究人员建议研究大尺度大气和海洋流动的结构、其鲁棒性/稳定性和过渡，以更好地了解与其低频变化的典型来源相关的大气和海洋预测和可预测性。拟议的努力研究在两个相互关联的领域的特定主题：A）不可压缩和地球物理流体流动的几何理论，和B）大气和海洋流动的低频变化。在第一个领域的拟议工作重点是不可压缩的和地球物理的流体流动在底层的物理空间的结构转变。第二个领域的拟议工作侧重于环流尺度海洋环流的分叉问题。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。 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 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.