A ridge tracking algorithm and error estimate for efficient computation of Lagrangian coherent structures

A ridge tracking algorithm for the computation and extraction of Lagrangian coherent structures (LCS) is developed. This algorithm takes advantage of the spatial coherence of LCS by tracking the ridges which form LCS to avoid unnecessary computations away from the ridges. We also make use of the temporal coherence of LCS by approximating the time dependent motion of the LCS with passive tracer particles. To justify this approximation, we provide an estimate of the difference between the motion of the LCS and that of tracer particles which begin on the LCS. In addition to the speedup in computational time, the ridge tracking algorithm uses less memory and results in smaller output files than the standard LCS algorithm. Finally, we apply our ridge tracking algorithm to two test cases, an analytically defined double gyre as well as the more complicated example of the numerical simulation of a swimming jellyfish. In our test cases, we find up to a 35 times speedup when compared with the standard LCS algorithm.