Trajectory-Augmented Visualization of Lagrangian Coherent Structures in Unsteady Flow

The finite-time Lyapunov exponent (FTLE) field can be used for many purposes, from the analysis of the predictability in dynamical systems to the topological analysis of timedependent vector fields. In the topological context, the topic of this work, FTLE ridges represent Lagrangian coherent structures (LCS), a counterpart to separatrices in vector field topology. Since the explicit vector field behavior cannot be deduced from these representations, they may be augmented by line integral convolution patterns, a computational flow visualization counterpart to the surface oil flow method. This is, however, strictly meaningful only in stationary vector fields. Here, we propose an augmentation that visualizes the LCS-inducing flow behavior by means of complete trajectories but avoids occlusion and visual clutter. For this we exploit the FTLE for both the selection of significant trajectories as well as their individual representation. This results in 3D line representations for 2D vector fields by treating 2D time-dependent vector fields in 3D space-time. We present two variants of the approach, one easing the choice of the finite advection time for FTLE analysis and one for investigating the flow once the time is chosen.