Theoretic Studies in Geophysical Fluid Dynamics and Climate Dynamics

该奖项是根据2009年美国复苏和投资法案（公法111-5）资助的。研究者研究与大气和海洋流动的低频变率有关的因素，这些因素在气候变化中起作用。他着重研究了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潜在的问题，另一方面，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分岔理论——这些理论应用于物理问题。这些新理论也适用于非线性科学和工程中的其他问题。动态过渡理论的主要思想是寻找完整的过渡态集合，给出稳定和过渡的完整表征。过渡状态的集合——物理“现实”——由一个局部吸引子表示。沿着这条线，发展了动态过渡理论来识别过渡状态，并对它们进行动态和物理分类。该项目涉及与不同机构的大气/海洋科学家的具体合作，并包括对研究生的培训。研究者研究了一些典型的气候变率源，它们在气候变化中独立地和相互作用地发挥着重要作用。风驱动的环流主要在海洋的亚年际-年际变化中起作用，厄尔尼诺南方涛动与年际变化有关，而温盐环流在十年-千年变化中最重要。研究者对这些现象进行了仔细的基本层面的检查。研究生也参与了这个项目。这些研究可以改善对天气、气候和环境现象的预测，并对这些对我们的经济至关重要的现象有新的认识。

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.