We propose a dynamical systems approach to the study of weak turbulence(spatiotemporal chaos) based on the periodic orbit theory, emphasizing
the role of recurrent patterns and coherent structures. After a brief review of the periodic orbit theory and its application to low-dimensional dynamics, we discuss its possible extension to study dynamics of spatially extended systems. The discussion is three-fold. First, we introduce a novel variational scheme for finding periodic orbits in high-dimensional systems.
Second, we prove rigorously the existence of periodic structures (modulated amplitude waves) near the first instability of the complex Ginzburg-Landau equation, and check their role
in pattern formation. Third, we present the extensive numerical exploration of the Kuramoto-Sivashinsky system in the chaotic regime: structure of the equilibrium solutions, our search for the shortest periodic orbits, description of the chaotic invariant set in terms of intrinsic coordinates and return maps on the Poincare section.
| Identifer | oai:union.ndltd.org:GATECH/oai:smartech.gatech.edu:1853/4833 |
| Date | 19 November 2004 |
| Creators | Lan, Yueheng |
| Publisher | Georgia Institute of Technology |
| Source Sets | Georgia Tech Electronic Thesis and Dissertation Archive |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation |
| Format | 1909317 bytes, application/pdf |
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