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SPACE-TIME VISUALIZATION OF DYNAMICS IN LAGRANGIAN COHERENT STRUCTURES OF TIME-DEPENDENT 2D VECTOR FIELDSTopics: Flow Visualization; Vector/Tensor Field Visualization

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Subjects/Areas/Topics:Computer Vision, Visualization and Computer Graphics
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Flow Visualization
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Spatial Data Visualization
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Vector/Tensor Field Visualization

Abstract: Lagrangian coherent structures (LCS), apparent as ridges in the finite-time Lyapunov exponent (FTLE) field, represent a time-dependent alternative to the concept of separatrices in vector field topology. Traditionally, LCS are analyzed and visualized in terms of their geometric shape only, neglecting stretching and compression in tangent directions. These effects are, however, of particular interest in mixing phenomena and turbulence. Hyperbolicity plays an important role in these processes and gives rise to hyperbolic trajectories originating at
the intersections of forward and reverse LCS. Since integration of hyperbolic trajectories is difficult, we propose to visualize the corresponding space-time intersection curves of LCS instead. By stacking the traditional 2D FTLE video frames of time-dependent vector fields, a space-time FTLE field is obtained. In this field, ridge lines turn into ridge surfaces representing LCS, and their intersection forms curves that are a robust alternative to hyperbolic trajectories. Additionally, we use a space-time representation of the time-dependent vector field, leading to a steady 3D space-time vector field. In this field, the LCS become stream surfaces given that their advection property is sufficiently met. This makes visualization of the dynamics within LCS amenable to line integral convolution (LIC), conveying in particular the dynamics around hyperbolic trajectories. To avoid occlusion, the LCS can be constrained to space-time bands around the intersection curves, resembling visualization by saddle connectors. We evaluate our approach using synthetic, simulated, and measured vector fields.(More)

Lagrangian coherent structures (LCS), apparent as ridges in the finite-time Lyapunov exponent (FTLE) field, represent a time-dependent alternative to the concept of separatrices in vector field topology. Traditionally, LCS are analyzed and visualized in terms of their geometric shape only, neglecting stretching and compression in tangent directions. These effects are, however, of particular interest in mixing phenomena and turbulence. Hyperbolicity plays an important role in these processes and gives rise to hyperbolic trajectories originating at the intersections of forward and reverse LCS. Since integration of hyperbolic trajectories is difficult, we propose to visualize the corresponding space-time intersection curves of LCS instead. By stacking the traditional 2D FTLE video frames of time-dependent vector fields, a space-time FTLE field is obtained. In this field, ridge lines turn into ridge surfaces representing LCS, and their intersection forms curves that are a robust alternative to hyperbolic trajectories. Additionally, we use a space-time representation of the time-dependent vector field, leading to a steady 3D space-time vector field. In this field, the LCS become stream surfaces given that their advection property is sufficiently met. This makes visualization of the dynamics within LCS amenable to line integral convolution (LIC), conveying in particular the dynamics around hyperbolic trajectories. To avoid occlusion, the LCS can be constrained to space-time bands around the intersection curves, resembling visualization by saddle connectors. We evaluate our approach using synthetic, simulated, and measured vector fields.

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Bachthaler S., Sadlo F., Dachsbacher C. and Weiskopf D. (2012). SPACE-TIME VISUALIZATION OF DYNAMICS IN LAGRANGIAN COHERENT STRUCTURES OF TIME-DEPENDENT 2D VECTOR FIELDS.In Proceedings of the International Conference on Computer Graphics Theory and Applications and International Conference on Information Visualization Theory and Applications - Volume 1: IVAPP, (VISIGRAPP 2012) ISBN 978-989-8565-02-0, pages 573-583. DOI: 10.5220/0003810905730583

@conference{ivapp12, author={Sven Bachthaler and Filip Sadlo and Carsten Dachsbacher and Daniel Weiskopf}, title={SPACE-TIME VISUALIZATION OF DYNAMICS IN LAGRANGIAN COHERENT STRUCTURES OF TIME-DEPENDENT 2D VECTOR FIELDS}, booktitle={Proceedings of the International Conference on Computer Graphics Theory and Applications and International Conference on Information Visualization Theory and Applications - Volume 1: IVAPP, (VISIGRAPP 2012)}, year={2012}, pages={573-583}, publisher={SciTePress}, organization={INSTICC}, doi={10.5220/0003810905730583}, isbn={978-989-8565-02-0}, }

TY - CONF

JO - Proceedings of the International Conference on Computer Graphics Theory and Applications and International Conference on Information Visualization Theory and Applications - Volume 1: IVAPP, (VISIGRAPP 2012) TI - SPACE-TIME VISUALIZATION OF DYNAMICS IN LAGRANGIAN COHERENT STRUCTURES OF TIME-DEPENDENT 2D VECTOR FIELDS SN - 978-989-8565-02-0 AU - Bachthaler S. AU - Sadlo F. AU - Dachsbacher C. AU - Weiskopf D. PY - 2012 SP - 573 EP - 583 DO - 10.5220/0003810905730583