Localized Finite-time Lyapunov Exponent for Unsteady Flow Analysis

The Finite-time Lyapunov Exponent (FTLE) is a measure for the rate of separation of particles in time-dependent flow fields. It provides a valuable tool for the analysis of unsteady flows. Commonly it is defined based on the flow map, analyzing the separation of trajectories of nearby particles over a finite-time span. This paper proposes a localized definition of the FTLE using the Jacobian matrix along a pathline as generator of the separation. The localized FTLE (L-FTLE) definition makes only use of flow properties along the pathline. A fast computation algorithm is presented that efficiently reuses FTLE values from previous time steps, following an idea similar to FastLIC. The properties of L-FTLE are analyzed with focus on the sensitivity to the parameters of the algorithm. It is further compared to the flow map based version under consideration of robustness to noise.