This project will study the general area of instability in various physical systems using advanced mathematical concepts from perturbation theory, dynamical systems theory and Hamiltonian mechanics. Among the topics to be considered are the stability of dispersive wave solutions of the Ginzburg-Landau equation and the Zakharov equation, the advective mixing of fluid trajectories at the onset of chaos in viscous flows and the escape of particle trajectories of rotating Hamiltonian systems from KAM regions. The phenomenon of turbulence is perhaps the most important and the most difficult problem in fluid dynamics today. In this project the principal investigator will study simple models of turbulent flows using techniques from perturbation theory and nonlinear mechanics in order to understand better how instabilities in flows are magnified to the point where the flows go completely unstable and become turbulent. This too is an important problem, predicting where and when a flow first becomes turbulent, since very often one wants to delay the onset of turbulence for as long as possible.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
9000593
Program Officer
Alan Izenman
Project Start
Project End
Budget Start
1990-05-15
Budget End
1991-10-31
Support Year
Fiscal Year
1990
Total Cost
$18,500
Indirect Cost
Name
University of Illinois Urbana-Champaign
Department
Type
DUNS #
City
Champaign
State
IL
Country
United States
Zip Code
61820