Theoretic Studies in Geophysical Fluid Dynamics and Climate Dynamics

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In this project, the PI will study large scale atmospheric and oceanic flows, with the goal of understanding their structure, robustness and stability in order to improve their predictability, in particular with respect to their low-frequency variability. The project will continue to develop the PI's dynamic transition theory for both deterministic and random dissipative systems, and apply this to the study of dynamic transitions and pattern formations in atmospheric and oceanic geophysical flows. Such flows include the wind driven ocean circulation, the meridional overturning oceanic circulation, and the tropical atmosphere-ocean modes associated with the El Nino Southern Oscillations (ENSO). Their variability, independently and interactively, may play a significant role in climate changes, past and future. A combination of physical modeling, asymptotic methods, rigorous mathematical theory, and large scale computing will be used to yield new insights into physical phenomena. The mathematical models in the project are based on partial differential equations, which can be put into the perspective of dissipative systems. The dynamic transitions of such dissipative systems are then classified as continuous, catastrophic or random. The project involves specific collaborations with active atmosphere/ocean scientists in different institutions. Graduate students will be involved in the project as well.In this project, the PI and his collaborators will work on mathematical models for large scale climate phenomena such as the El Nino Southern Oscillations (ENSO), with the goal of understanding their long term variability. A recently developed dynamic transition theory will be employed for this purpose. The approach allows one to look at the full set of transition states, e.g. the onset of an El Nino or a La Nina episode. By identifying such transition states and classifying them both mathematically and physically, possible physical mechanisms for such phenomena can be identified or perhaps ruled out. The proposed research involves specific collaborations with active atmosphere/ocean scientists in different institutions, and it is expected that the proposed studies will lead to improved predictions and new insights of weather, climate, and environmental phenomena of central importance to our economy. Also, graduate students are partially involved in the proposed project.