Session AM - Chaos and Fractals.
ORAL session, Sunday morning, November 23
Saratoga, SMH
It has been shown that certain fluid motions have sufficient topological complexity for chaos to be `built in' to the system without regard for the details of the dynamics. The key to the analysis lies in classifying the motion of boundaries or periodic points according to the Thurston-Nielsen classification theorem. The theory provides a lower bound on the material stretch rate in the flow field, and recent investigations in Stokes flow suggest that this lower bound is physically significant. The ability of the theory to provide a useful quantitative bound on stretching without much knowledge of the dynamics makes this an attractive tool for achieving mixing enhancement in laminar flows. However, while investigations of topological chaos are increasing, the connection between the topological theory and the details of the corresponding fluid motion is still not clear. We will discuss the occurrence, characteristics, and importance of topological chaos in various laminar flows.