Lagrangian Coherent Structures: Nature's Transport Barriers

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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Lagrangian coherent structures and plasma transport processes

Journal of Plasma Physics ◽

10.1017/s0022377815000690 ◽

2015 ◽

Vol 81 (5) ◽

Cited By ~ 11

Author(s):

M. V. Falessi ◽

F. Pegoraro ◽

T. J. Schep

Keyword(s):

Dynamical System ◽

Phase Space ◽

Coherent Structures ◽

Transport Processes ◽

Lagrangian Coherent Structures ◽

Plasma Transport ◽

Periodic Systems ◽

Transport Barriers ◽

Definition Of ◽

General Time

A dynamical system framework is used to describe transport processes in plasmas embedded in a magnetic field. For periodic systems with one degree of freedom, the Poincaré map provides a splitting of the phase space into regions where particles have different kinds of motion: periodic, quasi-periodic or chaotic. The boundaries of these regions are transport barriers, i.e. a trajectory cannot cross such boundaries throughout the evolution of the system. Lagrangian coherent structures generalize this method to systems with the most general time dependence, splitting the phase space into regions with different qualitative behaviours. This leads to the definition of finite-time transport barriers, i.e. trajectories cannot cross the barrier for a finite amount of time. This methodology can be used to identify fast recirculating regions in the dynamical system and to characterize the transport between them.

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Dynamic groundwater management using Lagrangian coherent structures

10.5194/egusphere-egu2020-7883 ◽

2020 ◽

Author(s):

Michel Speetjens ◽

Stephen Varghese

Keyword(s):

Groundwater Management ◽

Coherent Structures ◽

Operating Conditions ◽

Water Bodies ◽

Lagrangian Coherent Structures ◽

Scalar Transport ◽

Subsurface Water ◽

Transport Barriers ◽

In Situ Processing

Scope is scalar transport in enhanced subsurface flows driven via injection and extraction wells. An important application of this concept is found in groundwater treatment by containment and remediation of polluted groundwater via so-called &#8220;permeable reactive treatment zones&#8221; (PRTZs) and &#8220;permeable reactive barriers&#8221; (PRBs). Climate change introduces new challenges to clean and safe water as intrusion of seawater or contaminants into water catchment areas by rising sea levels or changing subsurface flow patterns. This necessitates groundwater management that enables shielding and containment of subsurface water bodies under dynamic conditions. However, this is beyond the above conventional water-treatment technologies; PRTZs and PRBs are namely created through a &#8220;screen&#8221; of injected reactants, construction of infiltration trenches or establishment of subsurface &#8220;ice walls&#8221; and thus static and inflexible to unforeseen or changing circumstances.&#160;This study explores an in situ processing strategy that relies on the existence of so-called &#8220;Lagrangian coherent structures&#8221; (LCSs) forming in the fluid trajectories and governing the advective transport in the reservoir. Such LCSs emerge naturally in (subsurface) flow systems and admit rapid and accurate control by the pumping scheme for the wells. Moreover, LCSs are fundamentally embedded in the transport of scalar quantities (e.g. reactants or heat) even in case of significant diffusion and/or chemical reactivity. Thus LCSs act as &#8220;internal actuators&#8221; for scalar transport and can be utilized for the creation of dynamic processing zones, reaction fronts and transport barriers in a wide range of operating conditions. LCS-based in situ processing may offer a promising alternative to conventional methods for groundwater management by enabling dynamic shielding and containment of subsurface water bodies without the need for physical (and static) boundaries as in PRTZs and PRBs.&#160;The concept of dynamic in situ processing using LCSs is demonstrated by the advective-diffusive scalar transport in a two-dimensional (2D) unsteady Darcy flow in a circular reservoir driven by an array of injection/extraction wells. To this end the non-trivial link between scalar and Lagrangian transport is rigorously established via methods from dynamical-systems theory. This enables systematic demarcation and characterization of confinement zones and transport barriers as a function of (dynamic) operating conditions for the generic case of scalar transport subject to diffusion.

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Kinematic and magnetic coherent structures in solar and stellar turbulence

Proceedings of the International Astronomical Union ◽

10.1017/s1743921318001217 ◽

2018 ◽

Vol 13 (S340) ◽

pp. 285-288 ◽

Cited By ~ 1

Author(s):

Abraham C.-L. Chian ◽

Rodrigo A. Miranda ◽

Erico L. Rempel ◽

Brigitte Schmieder

Keyword(s):

Magnetic Flux ◽

Coherent Structures ◽

Phase Synchronization ◽

High Accuracy ◽

Lagrangian Coherent Structures ◽

The Novel ◽

Magnetorotational Instability ◽

Flux Tubes ◽

Transport Barriers ◽

Magnetic Flux Tubes

AbstractWe show that on-off intermittency in solar and stellar cycles is a result of amplitude-phase synchronization in multiscale interactions in solar/stellar dynamos or magnetorotational instability which leads to the formation of kinematic and magnetic coherent structures, and the novel techniques of Lagrangian coherent structures can detect transport barriers and vortices such as magnetic flux tubes/ropes in solar and stellar turbulence with high accuracy.

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Coherent structures and magnetic reconnection in photospheric and interplanetary magnetic field turbulence

Proceedings of the International Astronomical Union ◽

10.1017/s1743921320000113 ◽

2019 ◽

Vol 15 (S354) ◽

pp. 351-354

Author(s):

Rodrigo A. Miranda ◽

Abraham C.-L. Chian ◽

Erico L. Rempel ◽

Suzana S. A. Silva

Keyword(s):

Magnetic Field ◽

Solar Wind ◽

Magnetic Reconnection ◽

Interplanetary Magnetic Field ◽

Coherent Structures ◽

Lagrangian Coherent Structures ◽

Inertial Subrange ◽

Magnetic Elements ◽

Transport Barriers ◽

Magnetic Field Turbulence

AbstractIn this paper it is shown that rope-rope magnetic reconnection in the solar wind can enhance multifractality in the inertial subrange and drive intermittent magnetic field turbulence. Additionally, it is shown that Lagrangian coherent structures can unveil the transport barriers of magnetic elements in the quiet Sun.

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