Theoretic Studies in Geophysical Fluid Dynamics and Climate Dynamics

王DMS-0908051 该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。 该系统研究与大气和海洋流动的低频变率相关的因素，这些因素在气候变化中发挥作用。 他专注于大气和海洋变化的三个来源：风驱动的海洋环流，温盐环流和厄尔尼诺南方涛动（ENSO）。 这项研究一方面涉及应用现有的数学理论来理解基本问题，另一方面涉及进一步发展新的数学理论-动态转换理论、不可压缩流的几何理论和吸引子分叉理论-这些理论都应用于物理问题。这些新理论也可以应用于非线性科学和工程中的其他问题。 动态跃迁理论的主要思想是寻找跃迁态的全集，给出稳定性和跃迁的完整刻画。 过渡态的集合--物理“现实”--由局部吸引子表示。 在此基础上，发展了动态跃迁理论，对跃迁态进行了动态和物理的识别和分类。 该项目涉及与不同机构的大气/海洋科学家的具体合作，包括培训研究生。 研究人员研究了一些典型的气候变率源，这些源在气候变化中起着独立和相互作用的重要作用。 风驱动环流对海洋的年际变率起主要作用，厄尔尼诺南方涛动与年际变率有关，温盐环流对海洋的年代际变率起主要作用。 调查人员对这些现象进行了仔细的基本检查。 研究生参与了这个项目。 这些研究可能会改善对天气、气候和环境现象的预测和新的见解，这些现象对我们的经济至关重要。

WangDMS-0908051 This award is funded under the American Recovery andReinvestment Act of 2009 (Public Law 111-5). The investigatorstudies factors that are relevant to the low-frequencyvariability of atmospheric and oceanic flows and that play a rolein climate changes. He focuses on three sources of atmosphericand oceanic variability: the wind-driven ocean circulation, thethermohaline circulation, and the El Nino Southern Oscillations(ENSO). The study involves, on the one hand, applications ofexisting mathematical theory to the understanding of theunderlying problems, and, on the other hand, the furtherdevelopment of new mathematical theories -- dynamic transitiontheory, geometric theory for incompressible flows, and attractorbifurcation theory -- that are applied to the physical problems. These new theories also have application to other problems innonlinear science and engineering. The main idea of dynamictransition theory is to search for the full set of transitionstates, giving a complete characterization of stability andtransition. The set of transition states -- physical "reality"-- is represented by a local attractor. Following this line,dynamic transition theory is developed to identify the transitionstates and to classify them both dynamically and physically. Theproject involves specific collaborations with atmosphere/oceanscientists in different institutions and includes training ofgraduate students. The investigator studies some typical sources of climatevariability, which, independently and interactively, play asignificant role in climate changes. Wind-driven circulationplays a role mostly in the oceans' subannual-to-interannualvariability, the El Nino Southern Oscillations are associatedwith interannual variability, and the thermohaline circulation ismost important in decadal-to-millenial variability. Theinvestigator undertakes a careful fundamental-level examinationof these phenomena. Graduate students are involved in theproject. The studies could lead to improved predictions of andnew insights into weather, climate, and environmental phenomenaof central importance to our economy.