Shadden, S., F. Lekien, and J. E. Marsden
Previous work has demonstrated the usefulness of FTLE fields and the associated LCSs for revealing the Lagrangian behavior of systems with general time dependence. However, ridges of the FTLE field need not be exactly advected with the flow. The main result of this paper is an estimate for the flux across an LCS, which shows that the flux is small, and in most cases negligible, for well-defined LCSs or those that rotate at a speed comparable to the local Eulerian velocity field, and are computed from FTLE fields with a sufficiently long integration time. Under these hypotheses, the structures represent nearly invariant manifolds even in systems with arbitrary time dependence.
The results are illustrated on three examples. The first is a simplified dynamical model of a double-gyre flow. The second is surface current data collected by high-frequency radar stations along the coast of Florida and the third is unsteady separation over an airfoil. In all cases, the existence of LCSs governs the transport and it is verified numerically that the flux of particles through these distinguished lines is indeed negligible.