CDS/CIMMS Lunctime Series Seminar: Separation and Coherent Structures in Time-Chaotic Flows

Francois Lekien, Princeton University
Mechanical and Aerospace Engineering

In autonomous and time-periodic dynamical systems, transport and mixing can be studied using the stable and unstable manifolds of hyperbolic fixed points and periodic orbits. Numerous experiments have revealed the presence of similar coherent structures in aperiodic systems. These mixing templates are usually invisible to the naked eye but can be extracted, for example, by computing finite-time Lyapunov exponents or finite-time hyperbolic invariant manifolds. These structures indicate alleyways and barriers to transport and provide a geometric description of the mixing processes in the system.

In recent years, there has been much effort in applying this methodology to the study of mixing in fluids and geophysical flows. Indeed, these systems are strongly aperiodic and do not have, in general, fixed points or periodic orbits. In this talk, I will describe fluid transport in Monterey Bay. High-frequency radar stations provide current measurements in real-time for the bay and permit the computation of dynamical barriers and alleyways in this complex system. The coherent structures reveal the existence of optimal release windows in which contaminants can be efficiently advected away from the coast, reducing their negative impact on the marine environment. In addition, the alleyways can be used to optimize the deployment of drifters and the routes of
underwater vehicles to maximize coverage of an area.

Transport and mixing near a coastline can also be studied in terms of separation and re-attachment profiles attached to the boundary. I will discuss how to obtain exact criteria to detect and control separation points and related separation profiles in Monterey Bay. Jet-actuated systems can control their separation points to a desired location and fine-tune the lift on an airfoil, or transport fuel efficiently along separation profiles. For drifters and underwater vehicles in the ocean, weak actuators, such as a rudder or a deformable rogue, can be used to control the effective separation points seen by the vehicle. Such controllers do not "fight the currents". They take advantage of the strong hyperbolic structures that are present in the ocean, require less energy, and increase the time that the vehicle spends at sea.