 |
Center for Nonlinear Studies |
The orbits of fluid particles in two dimensions effectively act as topological obstacles to material lines. A spacetime plot of the orbits of such particles is a braid whose properties reflect the underlying dynamics. For a chaotic flow, the braid generated by the motion of three or more fluid particles is computed. A ``braiding exponent'' is defined to characterize the complexity of the braid. This exponent is proportional to the usual Lyapunov exponent of the flow. Measuring chaos and mixing properties in this manner has several advantages, since neither nearby trajectories nor derivatives of the velocity field are needed.
Host: D Holm, CCS-2