A 3D fast algorithm for computing Lagrangian coherent structures via ridge tracking

Abstract

Lagrangian coherent structures (LCS) in fluid flows appear as co-dimension one ridges of the finite time Lyapunov exponent (FTLE) field. In three- dimensions this means two-dimensional ridges. A fast algorithm is presented here to locate and extract such ridge surfaces while avoiding unnecessary computations away from the LCS. This algorithm reduces the order of the computational complexity from O(1/dx^3) to about O(1/dx^2) by eliminating computations over most of the three dimensional domain and computing the FTLE only near the two-dimensional ridge surfaces. The algorithm is grid based and proofs of error bounds for ridge locations are included. The algorithm performance and error bounds are verified in several examples. The algorithm offers significant advantages in computational cost as well as later data analysis.