Visualizing Lagrangian Coherent Structures and Comparison to Vector Field Topology

The transitional phase from local to global chaos in the magnetic field of a reconnecting current layer is investigated. Regions where the magnetic field is stochastic exist next to regions where the field is more regular. In regions between stochastic layers and between a stochastic layer and an island structure, the field of the finite time Lyapunov exponent (FTLE) shows a structure with ridges. These ridges, which are special gradient lines that are transverse to the direction of minimum curvature of this field, are approximate Lagrangian coherent structures (LCS) that act as barriers for the transport of field lines.

show abstract

“…It has be shown that in the case of finite Lyapunov exponent ridges, this leads to significant, consistent, and reliable visualizations. 16 …”

Section: Lcsmentioning

confidence: 99%

Barriers in the transition to global chaos in collisionless magnetic reconnection. I. Ridges of the finite time Lyapunov exponent field

et al. 2011

View full text Add to dashboard Cite

show abstract

“…by Goldhirsch et al in 1987 [8] for measuring predictability, see Yoden et al [30] for details. For steady vector fields LCS is comparable to vector field topology [9], although it tends to convey more information [25]. However, LCS is still well defined and interpretable for unsteady vector fields due to its Lagrangian definition, whereas classical vector field topology is only able to give an instantaneous view, except for the approaches by Theisel et al [29] and Shi et al [27] based on path lines.…”

Section: Introductionmentioning

confidence: 94%

“…Here some filtering criteria for ridges are recapitulated, and discussed in the context of adaptive ridge extraction, that have already been presented in [25] for ridge extraction in FTLE fields.…”

Section: Ridge Filteringmentioning

confidence: 99%

“…It is therefore our preferred method for filtering finite Lyapunov exponent ridges. The reader is referred to [25] for further details on the influence of this filtering criterion. Another natural criterion for filtering ridge regions is to prescribe a maximum for the second derivative λ n across the ridge, which results in suppressing regions with too "flat" ridge property:…”

Section: Ridge Filteringmentioning

confidence: 99%

“…LCS have played only a minor role in the field of scientific visualization until now. Two examples are direct visualization of 2-dimensional FTLE by Garth et al [7] and the visualization of ridges in 3-dimensional FTLE by the authors [25]. Section 2 gives some background on ridge extraction and ridge filtering.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Efficient Visualization of Lagrangian Coherent Structures by Filtered AMR Ridge Extraction

Sadlo

Peikert

2007

IEEE Trans. Visual. Comput. Graphics

Self Cite

155

107

View full text Add to dashboard Cite

Abstract-This paper presents a method for filtered ridge extraction based on adaptive mesh refinement. It is applicable in situations where the underlying scalar field can be refined during ridge extraction. This requirement is met by the concept of Lagrangian coherent structures which is based on trajectories started at arbitrary sampling grids that are independent of the underlying vector field. The Lagrangian coherent structures are extracted as ridges in finite Lyapunov exponent fields computed from these grids of trajectories. The method is applied to several variants of finite Lyapunov exponents, one of which is newly introduced. High computation time due to the high number of required trajectories is a main drawback when computing Lyapunov exponents of 3-dimensional vector fields. The presented method allows a substantial speed-up by avoiding the seeding of trajectories in regions where no ridges are present or do not satisfy the prescribed filter criteria such as a minimum finite Lyapunov exponent.

show abstract

The influence of cam geometry and operating conditions on chaotic mixing of viscous fluids in a twin cam mixer

Robinson

Cleary

2011

AIChE Journal

View full text Add to dashboard Cite

in Wiley Online Library (wileyonlinelibrary.com).Smooth particle hydrodynamica (SPH) simulations were used to better understand the mixing performance of a class of two-dimensional Twin Cam mixers. The chaotic manifolds of the flow are used to describe the mixing and to identify isolated regions. For an equilateral triangle cam geometry, a figure-eight manifold structure traps a layer of fluid against the cam boundaries. Changes in the differential rotation and phase offsets between the cams results in modest improvements in the mixing rate across the manifold barrier. Reducing the apex angle of the triangle changes the manifold structure and allows the trapped layer of fluid to mix more effectively with the rest of the domain. This article shows that examining the chaotic manifolds within a typical industrial mixer can provide valuable insight into both the transient and longterm mixing processes, leading to a more focused exploration of possible mixer configurations and to practical improvements in mixing efficiency.

show abstract

Visualizing Lagrangian Coherent Structures and Comparison to Vector Field Topology

Cited by 46 publications

References 8 publications

Barriers in the transition to global chaos in collisionless magnetic reconnection. I. Ridges of the finite time Lyapunov exponent field

Barriers in the transition to global chaos in collisionless magnetic reconnection. I. Ridges of the finite time Lyapunov exponent field

Efficient Visualization of Lagrangian Coherent Structures by Filtered AMR Ridge Extraction

The influence of cam geometry and operating conditions on chaotic mixing of viscous fluids in a twin cam mixer

Contact Info

Product

Resources

About