Theoretic Studies in Geophysical Fluid Dynamics and Climate Dynamics

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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.