Accession Number : ADA306758

Title :   Computational Study of Chaotic and Ordered Solutions of the Kuramoto-Sivashinsky Equation.

Descriptive Note : Contract rept.,

Corporate Author : INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA

Personal Author(s) : Smyrlis, Yiorgos S. ; Papageorgiou, Demetrios T.

PDF Url : ADA306758

Report Date : FEB 1996

Pagination or Media Count : 35

Abstract : We report the results of extensive numerical experiments on the Kuramoto Sivashinsky equation in the strongly chaotic regime as the viscosity parameter is decreased and increasingly more linearly unstable modes enter the dynamics. General initial conditions are used and evolving states do not assume odd parity. A large number of numerical experiments are employed in order to obtain quantitative characteristics of the dynamics. We report on different routes to chaos and provide numerical evidence and construction of strange attractors with self similar characteristics. As the 'viscosity' parameter decreases the dynamics becomes increasingly more complicated and chaotic. In particular it is found that regular behavior in the form of steady state or steady state traveling waves is supported amidst the time dependent and irregular motions. We show that multimodal steady states emerge and are supported on decreasing windows in parameter space. In addition we invoke a self-similarity property of the equation, to show that these profiles are obtainable from global fixed point attractors of the Kuramote Sivashinsky equation at much larger values of the viscosity.

Descriptors :   *CHAOS, *STATISTICAL MECHANICS, STEADY STATE, COMPUTATIONS, DYNAMICS, PARAMETERS, NUMERICAL ANALYSIS, TRAVELING WAVES.

Subject Categories : Thermodynamics

Distribution Statement : APPROVED FOR PUBLIC RELEASE