This paper proposes an algorithm to detect and characterize ridges in the finite time Lyapunov exponent (FTLE) field obtained from a continuous dynamical system or flow. These ridges represent time-dependent separatrices of the flow and are also called Lagrangian coherent structures (LCS). LCS have been demonstrated to be an effective way to analyze realistic time-chaotic flows, although they can be quite complex. Therefore, in order to exploit the information that LCS can provide it is important to locate and characterize these structures in a systematic way.
This can be accomplished by interpreting the FTLE as a height field and detecting the LCS as ridges of this graph.
Methodologies developed in the image processing framework are integrated with dynamical system inspired approaches in order to characterize ridge strength and location. The main novel contribution of the proposed algorithm is a scheme to connect sets of points into curves or surfaces (rather than distributions of points around a ridge axis) and classify these curves or surfaces using a dynamical systems measure of strength.
This approach provides the capability to track ranked LCS in space and time. Results are presented for a simple analytical model and noisy LCS from realistic three-dimensional geophysical fluid data.