Ridge Concepts for the Visualization of Lagrangian Coherent Structures

Schindler, Benjamin; Peikert, Ronald; Fuchs, Raphael; Theisel, Holger

doi:10.1007/978-3-642-23175-9_15

Cited by 34 publications

(38 citation statements)

References 22 publications

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“…r LCS approximations are a direct result of our algorithm and are obtained as piecewise linear curves (virtual paths). In contrast to existing FTLE methods, they require no post-processing such as ridge extraction [Ebe96,SPFT11].…”

Section: Discussionmentioning

confidence: 99%

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Time Line Cell Tracking for the Approximation of Lagrangian Coherent Structures with Subgrid Accuracy

Kühn

Engelke

Rössl

et al. 2013

Computer Graphics Forum

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Lagrangian coherent structures (LCSs) have become a widespread and powerful method to describe dynamic motion patterns in time-dependent flow fields. The standard way to extract LCS is to compute height ridges in the finite-time Lyapunov exponent field. In this work, we present an alternative method to approximate Lagrangian features for 2D unsteady flow fields that achieve subgrid accuracy without additional particle sampling. We obtain this by a geometric reconstruction of the flow map using additional material constraints for the available samples. In comparison to the standard method, this allows for a more accurate global approximation of LCS on sparse grids and for long integration intervals. The proposed algorithm works directly on a set of given particle trajectories and without additional flow map derivatives. We demonstrate its application for a set of computational fluid dynamic examples, as well as trajectories acquired by Lagrangian methods, and discuss its benefits and limitations.

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Section: Discussionmentioning

confidence: 99%

“…This is similar to the filtering of FLTE ridges, e.g. by separation strength [SPFT11]. Note that the particular topology of G at τ = 0 can be chosen arbitrarily, e.g.…”

Section: Cell Reconstructionmentioning

confidence: 96%

Time Line Cell Tracking for the Approximation of Lagrangian Coherent Structures with Subgrid Accuracy

Kühn

Engelke

Rössl

et al. 2013

Computer Graphics Forum

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“…4 While this definition lends itself to a point by point evaluation, it does not necessarily create connected lines forming ridges and attempts to amend the height ridge definition 29 resulted in an over-constrained system. 27 An alternative to the height ridge, the "watershed ridge" divides the system into disjoint regions based on global stationary points of the field. 4 The ridges are identified as slope lines, these being trajectories of the FTLE gradient field that connect the saddle points in the system to the local maxima.…”

Section: A Methodsmentioning

confidence: 99%

Refining finite-time Lyapunov exponent ridges and the challenges of classifying them

Allshouse

Peacock

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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While more rigorous and sophisticated methods for identifying Lagrangian based coherent structures exist, the finite-time Lyapunov exponent (FTLE) field remains a straightforward and popular method for gaining some insight into transport by complex, time-dependent two-dimensional flows. In light of its enduring appeal, and in support of good practice, we begin by investigating the effects of discretization and noise on two numerical approaches for calculating the FTLE field. A practical method to extract and refine FTLE ridges in two-dimensional flows, which builds on previous methods, is then presented. Seeking to better ascertain the role of a FTLE ridge in flow transport, we adapt an existing classification scheme and provide a thorough treatment of the challenges of classifying the types of deformation represented by a FTLE ridge. As a practical demonstration, the methods are applied to an ocean surface velocity field data set generated by a numerical model.

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“…In this example the flow field is two-dimensional, area preserving, and the velocity field is specified in space and time as it is derived from a known stream function. Advances in LCS (Poje and Haller 1999;Shadden et al 2005;Carlson et al 2010a;Aharon et al 2012;Schindler et al 2012) have used the time-dependent double gyre as a relatively simple demonstrative velocity field. The following definitions are taken from Shadden et al (2005) Here, we demonstrate defining integration options and initial positions, plotting trajectories, and visualizing LCS using single and multiple particle metrics.…”

Section: Double Gyrementioning

confidence: 99%

The particle tracking and analysis toolbox (PaTATO) for Matlab

Fredj

Carlson

Amitai

et al. 2016

Limnol. Oceanogr. Methods

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Lagrangian particle tracking and Lagrangian coherent structures (LCS) analysis tools aid in the studies of fluid flow and are especially helpful in understanding the role of transport in marine ecosystems. However, most existing particle tracking and analysis tools operate in conjunction with a specific model and/or require execution in multiple programming languages. The Particle Tracking and Analysis TOolbox (PaTATO) for Matlab aims to increase the availability of particle tracking and analysis techniques to a wider audience. PaTATO is compatible with many different types of velocity data and can compute forward and backward trajectories in two and/or three dimensions. PaTATO can compute standard LCS metrics, like Lyapunov exponents and relative dispersion, as well as the maximal extent of a trajectory (MET), a relatively new metric. Most importantly, PaTATO is computationally efficient and easy-to-use. We describe PaTATO, and present examples using the time-periodic double gyre, high frequency radar surface current observations, the Massachusetts Institute of Technology general circulation model (MITgcm), altimeter-derived geostrophic velocities (AVISO), and Nucleous for European Modelling of the Ocean (NEMO).Lagrangian particle tracking tools are commonly used in oceanography and limnology to study transport and mixing of tracers by observed or modeled fluid flows. Example applications include ocean mixing (Poje and Haller

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Ridge Concepts for the Visualization of Lagrangian Coherent Structures

Cited by 34 publications

References 22 publications

Time Line Cell Tracking for the Approximation of Lagrangian Coherent Structures with Subgrid Accuracy

Time Line Cell Tracking for the Approximation of Lagrangian Coherent Structures with Subgrid Accuracy

Refining finite-time Lyapunov exponent ridges and the challenges of classifying them

The particle tracking and analysis toolbox (PaTATO) for Matlab

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