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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Sadlo, F., Bachthaler, S., Dachsbacher, C., Weiskopf, D. (2013). Space-Time Flow Visualization of Dynamics in 2D Lagrangian Coherent Structures. In: Csurka, G., Kraus, M., Laramee, R.S., Richard, P., Braz, J. (eds) Computer Vision, Imaging and Computer Graphics. Theory and Application. Communications in Computer and Information Science, vol 359. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38241-3_10
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DOI: https://doi.org/10.1007/978-3-642-38241-3_10
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