Lagrangian coherent structures and mixing in two-dimensional turbulence

We introduce a Lagrangian definition for the boundaries of coherent structures in two-dimensional turbulence. The boundaries are defined as material lines that are linearly stable or unstable for longer times than any of their neighbors. Such material lines are responsible for stretching and folding in the mixing of passive tracers. We derive an analytic criterion that can be used to extract coherent structures with high precision from numerical or experimental data sets. The criterion provides a rigorous link between the Lagrangian concept of hyperbolicity, the Okubo-Weiss criterion, and vortex boundaries. We apply the results to simulations of two-dimensional barotropic turbulence.