Dynamical Systems and Nonlinear Control Theory
Mezic, Igor, Loire, S., Fonoberov, Vladimir A. and Hogan, P. (2010), "A New Mixing Diagnostic and Gulf Oil Spill Movement", Science: science.1194607.
Chaotic advection has served as the paradigm for mixing in fluid flows with simple time dependence. Its skeletal structure is based on analysis of invariant attracting and repelling manifolds in fluid flows. We develop a finite-time theory for two-dimensional incompressible fluid flows with arbitrary time dependence and introduce a new mixing diagnostic based on it. Besides stretching events around attracting and repelling manifolds, this allows us to detect hyperbolic mixing zones. We used the new diagnostic to forecast the spatial location and timing of oil washing ashore in Plaquemines Parish and Grand Isle, Louisiana, and Pensacola, Florida, in May 2010 and flow of oil towards Panama City Beach in June 2010.