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Recent advances enable the simultaneous computation of both attracting andrepelling families of Lagrangian Coherent Structures (LCS) at the same initialor final time of interest. Obtaining LCS positions at intermediate times,however, has been problematic, because either the repelling or the attractingfamily is unstable with respect to numerical advection in a given timedirection. Here we develop a new approach to compute arbitrary positions ofhyperbolic LCS in a numerically robust fashion. Our approach only involves theadvection of attracting material surfaces, thereby providing accurate LCStracking at low computational cost. We illustrate the advantages of thisapproach on a simple model and on a turbulent velocity data set.

Attraction-Based Computation of Hyperbolic Lagrangian Coherent Structures