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Ridge concepts for the visualization of Lagrangian coherent structures. (English) Zbl 1426.76590

Peikert, Ronald (ed.) et al., Topological methods in data analysis and visualization II. Theory, algorithms, and applications. Based on the 4th workshop on topology-based methods in data analysis and visualization, TopoInVis 2011, Zurich, Switzerland, April 4–6, 2011. Berlin: Springer. Math. Vis., 221-235 (2012).
Summary: The popularity of vector field topology in the visualization community is due mainly to the topological skeleton which captures the essential information on a vector field in a set of lines or surfaces separating regions of different flow behavior. Unfortunately, vector field topology has no straightforward extension to unsteady flow, and the concept probably most closely related to the topological skeleton are the so-called Lagrangian coherent structures (LCS). LCS are material lines or material surfaces that separate regions of different flow behavior. Ideally, such structures are material lines (or surfaces) in an exact sense and at the same time maximally attracting or repelling, but practical realizations such as height ridges of the finite-time Lyapunov exponent (FTLE) fulfill these two requirements only in an approximate sense. In this paper, we quantify the deviation from exact material lines/surfaces for several FTLE-based concepts, and we propose a numerically simpler variants of FTLE ridges that has equal or better error characteristics than classical FTLE height ridges.
For the entire collection see [Zbl 1231.00048].

MSC:

76M27 Visualization algorithms applied to problems in fluid mechanics
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