Georgia Institute of Technology College of Sciences

Building on recent work on hyperbolic barriers (generalized stable and unstable manifolds) and elliptic barriers (generalized KAM tori) for two-dimensional unsteady flows, we present Lagrangian descriptions of shearless barriers (generalized nontwist KAM tori) and barriers in higher dimensional flows. Shearless barriers (generalized nontwist KAM tori) capture the core of Rossby waves appearing in atmospheric and oceanic flows, and their robustness is appealing in the theory of magnetic confinement of plasma. For three-dimensional flows, we give a description of hyperbolic barriers as Lagrangian Coherent Structures (LCSs) that maximally repel in the normal direction, while shear barriers are LCSs that generate shear along the LCS and act as boundaries of Lagrangian vortices in unsteady fluid flows. The theory is illustrated on several models.