Dynamical Systems Theory for Geophysical Fluid Flows
Abstract
The PI explores both theoretical and operational aspects of dynamic transitions and non- Markovian parameterizing manifolds and applications to geophysical fluid dynamics and climate dynamics. One direction of the proposed work is to further develop the dynamic transition the-ory for both deterministic partial differential equations (PDEs) and stochastic partial differential equations (SPDEs). The main focuses are on 1) far-from equilibrium transitions, 2) classification of dynamic transitions of Stochastic PDEs, and 3) large excursions and large deviations of random dynamical systems, governed by stochastic dissipative PDEs. The second direction of the proposed effort is to develop theory and methods to explore lowdimensional non-Markovian stochastic reduction of the climate partial differential equations (PDEs) system, and to quantify the sensitivity and dynamic transitions of large-scale climate patterns and to improve the prediction of these patterns. The PI’s research has been to improve our basic understanding of important physical processes through a symbiotic interplay between advanced mathematics and physics. The proposed study involves, on the one hand, applications of the existing mathematical theory to the understanding of the underlying physical problems, and, on the other hand, the development of a new dynamical transition theory under close links to the physics. In return the theory is applied to the physical problems, leading to better understanding and to a number of new physical predictions for the underlying physical problems. The proposed work is based in part on the theory and methods developed by the PI in collaboration with Tian Ma, Mickael Chekroun and Honghu Liu, and on the collaborative efforts of the PI with leading e.g. geoscientists: Michael Ghil, Henk Dijkstra. The proposed effort will be achieved through the continued collaborations with them and potentially with Roger Samelson and David Neelin. It is expected that the new theory proposed will greatly advance the study of nonlinear dynamics for many problems in science and engineering. Also, it is hoped that the study of these physical problems will on the one hand provide a better understanding of the mechanisms and natures of geophysical fluid flows and climate, and on the other hand lead to improved predictions and new insights of weather, climate, and environmental phenomena of central importance to the ONR mission.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 12, 2016
- Source ID
- N000141512662
Entities
People
- Shouhong Wang
Organizations
- Indiana University
- Office of Naval Research
- United States Navy