Theoretic Studies in Geophysical Fluid Dynamics and Climate Dynamics

在这个项目中，PI将研究大尺度大气和海洋流动，目的是了解它们的结构、稳健性和稳定性，以便提高它们的可预测性，特别是关于它们的低频可变性。该项目将继续发展确定性耗散系统和随机耗散系统的PI动态转变理论，并将其应用于大气和海洋地球物理流动的动态转变和模式形成的研究。这种流动包括风驱动的海洋环流、经向翻转海洋环流和与厄尔尼诺南方振荡(ENSO)相关的热带大气-海洋模式。它们的可变性，独立和相互作用，可能在过去和未来的气候变化中发挥重要作用。物理模型、渐近方法、严格的数学理论和大规模计算的组合将被用来产生对物理现象的新见解。项目中的数学模型基于偏微分方程组，可以放在耗散系统的角度来考虑。然后将这种耗散系统的动态转变分为连续的、灾难性的或随机的。该项目涉及与不同机构中活跃的大气/海洋科学家的具体合作。研究生也将参与这个项目。在这个项目中，PI和他的合作者将致力于大范围气候现象的数学模型，如厄尔尼诺南方振荡(ENSO)，目的是了解它们的长期变异性。为此，将采用最近发展起来的动态跃迁理论。这种方法使人们能够看到整个过渡态的集合，例如厄尔尼诺或拉尼娜事件的开始。通过识别这种过渡态，并从数学和物理上对它们进行分类，可以识别或排除这种现象的可能物理机制。拟议的研究涉及与不同机构活跃的大气/海洋科学家的具体合作，预计拟议的研究将导致对对我们的经济至关重要的天气、气候和环境现象的更好的预测和新的见解。此外，研究生部分参与了拟议的项目。

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.