Deterministic and Stochastic Dynamics of Some Geophysical Systems

Illinois Institute Of Technology, Chicago IL

Investigators

Abstract

Duan 9973204 The investigator studies complex geophysical flow phenomena modeled by finite or infinite-dimensional deterministic or stochastic differential equations. The research focuses on transport and mixing in random geophysical flows, nonlocal transport in-geophysical flows, variational methods for geophysical models, and stochastic geophysical flow modelling. In the area of transport and mixing, the investigator quantifies fluid transport and mixing in geophysical flown by computing escape probability and mean resident time. The work on nonlocal transport studies-the mean advoctive and eddy transport of passive tracers or pollutants in geophysical flown, when the eddy diffusivity depends on time and space. For the research on variational methods for geophysical models, the investigator gains better ' uncftrotanding of the rotating shallow water dynamics, by studying steady patterns, spatial and temporal periodic patterns and homoclinic motions via emrging techniques in calculus of variations. Finally, he derives a simplified coupled atmosphere-ocean model by averaging over random wind forcing and over intrinsic fast waves, quantifies the approximation error of the averaged dynamics, and studies some aspects of the coupled atmosphere-ocean system using this averaged mod 1. The geophysical flows in the oceans and the atmosphere affect our environment and our society in profound ways. This project is motivated by the need of better scientific understanding of the environment and global change. The investigator takes random or uncertain effects into account to describe geophysical flows. He develops both daterministle.and stochastic, numerical and analytical techniques to understand complex geophysical flow phonanuma. This research improves our knowledge about dispersion, transport and mixing of pollutants in our environment, and about evolution and pattern formation of geophysical flows. The techniques resulting from this research are also useful in studying other emerging problem in engineering and