Abstract

Fluid flows that are spatiotemporally chaotic but not turbulent are hard to characterize and understand. This lecture will present new ways of describing such flows, in part to characterize their ability to produce mixing and transport.  (a) Complex flows can be characterized by their special topological points.  These special points can be detected and followed in real time by measuring the curvature of particle trajectories, and to use this information to study the transition to spatiotemporal chaos.  The special points are found to be pinned to the forcing when the driving is weak, but wander over the flow and interact in pairs when the flow is stronger.  Their behavior reveals a two-stage transition to spatiotemporal chaos: a gradual loss of spatial and temporal order followed by an abrupt onset of topological changes.  Another powerful way to describe complex flows is to determine their “stretching fields” (spatially resolved finite time Lyapunov exponent fields), which are very useful in describing mixing and reactions in fluid flows.