Lagrangian coherent structures and the smallest finite-time Lyapunov exponent

We introduce a definition of finite-time curvature evolution along with our recent study on shape coherence in nonautonomous dynamical systems. Comparing to slow evolving curvature preserving the shape, large curvature growth points reveal the dramatic change on shape such as the folding behaviors in a system. Closed trough curves of low finite-time curvature (FTC) evolution field indicate the existence of shape coherent sets, and troughs in the field indicate the most significant shape coherence. Here, we will demonstrate these properties of the FTC, as well as contrast to the popular Finite-Time Lyapunov Exponent (FTLE) computation, often used to indicate hyperbolic material curves as Lagrangian Coherent Structures (LCS). We show that often the FTC troughs are in close proximity to the FTLE ridges, but in other scenarios, the FTC indicates entirely different regions.

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Supergranular turbulence in the quiet Sun: Lagrangian coherent structures

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz1909 ◽

2019 ◽

Vol 488 (3) ◽

pp. 3076-3088 ◽

Cited By ~ 4

Author(s):

Abraham C-L Chian ◽

Suzana S A Silva ◽

Erico L Rempel ◽

Milan Gošić ◽

Luis R Bellot Rubio ◽

...

Keyword(s):

Coherent Structures ◽

Finite Time ◽

Local Maximum ◽

Lagrangian Coherent Structures ◽

Quiet Sun ◽

Finite Time Lyapunov Exponent ◽

Magnetic Elements ◽

Disc Centre ◽

Transport Barriers ◽

Intensity Images

ABSTRACT The quiet Sun exhibits a wealth of magnetic activities that are fundamental for our understanding of solar magnetism. The magnetic fields in the quiet Sun are observed to evolve coherently, interacting with each other to form prominent structures as they are advected by photospheric flows. The aim of this paper is to study supergranular turbulence by detecting Lagrangian coherent structures (LCS) based on the horizontal velocity fields derived from Hinode intensity images at disc centre of the quiet Sun on 2010 November 2. LCS act as transport barriers and are responsible for attracting/repelling the fluid elements and swirling motions in a finite time. Repelling/attracting LCS are found by computing the forward/backward finite-time Lyapunov exponent (FTLE), and vortices are found by the Lagrangian-averaged vorticity deviation method. We show that the Lagrangian centres and boundaries of supergranular cells are given by the local maximum of the forward and backward FTLE, respectively. The attracting LCS expose the location of the sinks of photospheric flows at supergranular junctions, whereas the repelling LCS interconnect the Lagrangian centres of neighbouring supergranular cells. Lagrangian transport barriers are found within a supergranular cell and from one cell to other cells, which play a key role in the dynamics of internetwork and network magnetic elements. Such barriers favour the formation of vortices in supergranular junctions. In particular, we show that the magnetic field distribution in the quiet Sun is determined by the combined action of attracting/repelling LCS and vortices.

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Local finite-time Lyapunov exponent, local sampling and probabilistic source and destination regions

Nonlinear Processes in Geophysics ◽

10.5194/npg-22-663-2015 ◽

2015 ◽

Vol 22 (6) ◽

pp. 663-677 ◽

Cited By ~ 7

Author(s):

A. E. BozorgMagham ◽

S. D. Ross ◽

D. G. Schmale

Keyword(s):

Lyapunov Exponent ◽

Coherent Structures ◽

Finite Time ◽

Large Scale ◽

Field Experiments ◽

Local Velocity ◽

Finite Time Lyapunov Exponent ◽

Independent Observations ◽

Large Scale Flow ◽

Local Sampling

Abstract. The finite-time Lyapunov exponent (FTLE) is a powerful Lagrangian concept widely used for describing large-scale flow patterns and transport phenomena. However, field experiments usually have modest scales. Therefore, it is necessary to bridge the gap between the concept of FTLE and field experiments. In this paper, two independent observations are discussed: (i) approximation of the local FTLE time series at a fixed location as a function of known distances between the destination (or source) points of released (or collected) particles and local velocity, and (ii) estimation of the distances between the destination (or source) points of the released (or collected) particles when consecutive release (or sampling) events are performed at a fixed location. These two observations lay the groundwork for an ansatz methodology that can practically assist in field experiments where consecutive samples are collected at a fixed location, and it is desirable to attribute source locations to the collected particles, and also in planning of optimal local sampling of passive particles for maximal diversity monitoring of atmospheric assemblages of microorganisms. In addition to deterministic flows, the more realistic case of unresolved turbulence and low-resolution flow data that yield probabilistic source (or destination) regions are studied. It is shown that, similar to deterministic flows, Lagrangian coherent structures (LCS) and local FTLE can describe the separation of probabilistic source (or destination) regions corresponding to consecutively collected (or released) particles.

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Transport and Mixing in Patient Specific Abdominal Aortic Aneurysms With Lagrangian Coherent Structures

ASME 2012 Summer Bioengineering Conference, Parts A and B ◽

10.1115/sbc2012-80475 ◽

2012 ◽

Cited By ~ 1

Author(s):

Amirhossein Arzani ◽

Shawn C. Shadden

Keyword(s):

Coherent Structures ◽

Abdominal Aortic Aneurysms ◽

Aortic Aneurysms ◽

Lagrangian Coherent Structures ◽

Patient Specific ◽

Complex Flow ◽

Flow Topology ◽

Finite Time Lyapunov Exponent ◽

Abdominal Aortic ◽

High Gradients

Abdominal aortic aneurysms (AAA) are characterized by disturbed flow patterns, low and oscillatory wall shear stress with high gradients, increased particle residence time, and mild turbulence. Diameter is the most common metric for rupture prediction, although this metric can be unreliable. We hypothesize that understanding the flow topology and mixing inside AAA could provide useful insight into mechanisms of aneurysm growth. AAA morphology has high variability, as with AAA hemodynamics, and therefore we consider patient-specific analyses over several small to medium sized AAAs. Vortical patterns dominate AAA hemodynamics and traditional analyses based on the Eulerian fields (e.g. velocity) fail to convey the complex flow structures. The computation of finite-time Lyapunov exponent (FTLE) fields and underlying Lagrangian coherent structures (LCS) help reveal a Lagrangian template for quantifying the flow [1].

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