Deterministic and Stochastic Dynamics of Some Geophysical Systems

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Duan9973204 The investigator studies complex geophysical flow phenomenamodeled by finite or infinite-dimensional deterministic orstochastic differential equations. The research focuses ontransport and mixing in random geophysical flows, nonlocaltransport in geophysical flows, variational methods forgeophysical models, and stochastic geophysical flow modeling. Inthe area of transport and mixing, the investigator quantifiesfluid transport and mixing in geophysical flows by computingescape probability and mean resident time. The work on nonlocaltransport studies the mean advective and eddy transport ofpassive tracers or pollutants in geophysical flows, when the eddydiffusivity depends on time and space. For the research onvariational methods for geophysical models, the investigatorgains better understanding of the rotating shallow waterdynamics, by studying steady patterns, spatial and temporalperiodic patterns and homoclinic motions via emerging techniquesin calculus of variations. Finally, he derives a simplifiedcoupled atmosphere-ocean model by averaging over random windforcing and over intrinsic fast waves, quantifies theapproximation error of the averaged dynamics, and studies someaspects of the coupled atmosphere-ocean system using thisaveraged model. The geophysical flows in the oceans and the atmosphereaffect our environment and our society in profound ways. Thisproject is motivated by the need of better scientificunderstanding of the environment and global change. Theinvestigator takes random or uncertain effects into account todescribe geophysical flows. He develops both deterministic andstochastic, numerical and analytical techniques to understandcomplex geophysical flow phenomena. This research improves ourknowledge about dispersion, transport and mixing of pollutants inour environment, and about evolution and pattern formation ofgeophysical flows. The techniques resulting from this researchare also useful in studying other emerging problems inengineering and applied sciences.