Abstract
Lagrangian coherent structures provide insight into unsteady fluid flow, but their construction has posed many challenges. These structures can be characterized as ridges of a field, but their local definition utilizes an ambiguous eigenvector direction that can point in one of two directions, and its ambiguity can lead to noise and other problems. We overcome these issues with an application of a global ridge definition, applied using the hierarchical watershed transformation. We show results on a mathematical flow model and a simulated vascular flow dataset indicating the watershed method produces less noisy structures.
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Notes
- 1.
The term watershed comes from hydrology, where it denotes a drainage basin region. Some texts that apply it to dataset analysis incorrectly use it to refer to the ridges separating these basins, and call the basins “catchment basins.” To avoid confusion, we will refer to ridges that separate regions.
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Acknowledgements
This work was supported in part by NSF Grants OCI-1047963 and OCI-1047764. We thank Siavash Ameli for his help with this project.
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Chen, M., Hart, J.C., Shadden, S.C. (2017). Hierarchical Watershed Ridges for Visualizing Lagrangian Coherent Structures. In: Carr, H., Garth, C., Weinkauf, T. (eds) Topological Methods in Data Analysis and Visualization IV. TopoInVis 2015. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-319-44684-4_14
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DOI: https://doi.org/10.1007/978-3-319-44684-4_14
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