F. Sadlo, S. Bachthaler, C. Dachsbacher, D. Weiskopf:

Space-Time Flow Visualization of Dynamics in 2D Lagrangian Coherent Structures

In Computer Vision, Imaging and Computer Graphics. Theory and Application, Springer Berlin Heidelberg, pp. 145–159, 2013.

Abstract

Stretching and compression in tangent directions of Lagrangian coherent structures (LCS) are of particular interest in the vicinity of hyperbolic trajectories and play a key role in turbulence and mixing. Since integration of hyperbolic trajectories is difficult, we propose to visualize them in 2D time-dependent vector fields by space-time intersection curves of LCS. LCS are present as ridge lines in the 2D finite-time Lyapunov exponent (FTLE) field and as ridge surfaces in its 3D space-time domain. We extract these ridge surfaces from the forward and reverse FTLE field and intersect them. Due to their advection property, LCS become stream surfaces in 3D space-time. This allows us to use line integral convolution on the LCS to visualize their intrinsic dynamics, in particular around hyperbolic trajectories. To reduce occlusion, we constrain the LCS to space-time bands around their intersection curves. We evaluate our approach using synthetic, simulated, and measured vector fields.

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