Theoretical Studies in Geophysical Fluid Dynamics

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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.