Hidden Coherence in Complex Flows

From environmental sciences to aerodynamic separation, fluid flows exhibit entangled stretching and
folding, leading to chaos. Using concepts from calculus of variations, geometry and fluid mechanics, I
discuss the development of mathematical methods that unveil the organizers of the dynamical systems’
phase space. While several stretching measures exist as Finite-time Lyapunov exponents, Cauchy--Green
and rate-of-strain tensors, less is known about folding. I will present analytic results for the evolution of
Lagrangian Folding of material lines and surfaces in 2D and 3D flows. I illustrate our results on
experimental data related to highly unsteady separated flows and search and rescue operations at sea. I
show how our techniques uncover previously unknown structures, including the onset of aerodynamic
separation and hidden short-term attractors on the ocean surface, currently adopted by the US Coast
Guard.