Dynamical characteristics of weak turbulence

This project is an exploration of dynamical features of chaotic physical systems with the emphasis upon turbulent fluids. The specific areas of investigation involve: (1) the development of techniques that discriminate measurable differences in the observed behavior of theoretical models for chaotic behavior, (2) the application of these techniques to experimental studies, and (3) the study of bifurcation behavior in multiparameter families of differential equations. The transition to chaotic behavior in fluids has received intense experimental study during the past ten years. Various routes to chaos have been studied, and a satisfying picture has emerged of how this transition proceeds in low dimensional dynamical systems. Our primary interest is in the behavior of a system after it has undergone the transition. Of central concern is the question of determining when low dimensional chaotic models provide a good description of the physical system.