Topology and stochasticity of turbulent magnetic fields

Jafari, Amir; Vishniac, Ethan T.

doi:10.1103/physreve.100.013201

Cited by 15 publications

(59 citation statements)

References 30 publications

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“…In this section, we introduce the theoretical tools to be employed in section 3, where we develop vector field topology. Most importantly, the concept of vector field complexity, equation (4) introduced recently in [11], and the time translation operator, equation (5), are briefly discussed.…”

Section: Vector Fieldsmentioning

confidence: 99%

“…In doing so, it turns out that the evolution of magnetic complexity is closely related to the spatial complexity of the velocity field, which provides a means to study the phenomena of magnetic reconnection and magnetic field generation in astrophysical bodies. For details see [11,12] and [13]. Appendix B also provides a general review of these recent developments.…”

Section: Spatial Complexitymentioning

confidence: 99%

“…The other complication arises due to the stochastic nature of field lines in real turbulent fluids e.g., in astrophysics. Only recently have these important facts taken into account in problems related to magnetic field generation, evolution and reconnection (see e.g., [9,11,15,16,13]). The mere purpose of briefly discussing these concepts here is to emphasize that the notion of field lines cannot be used in a rigorous manner to define or even visualize the topology of a time-dependent vector field.…”

Section: Field Linesmentioning

confidence: 99%

“…is continuous if f has compact support and is continuous, which implies that f is uniformly continuous. turbulence will in general indicate that the velocity and magnetic fields are also Hölder singular [11], therefore, real magnetic fields e.g., on the solar surface, are expected to change their topology frequently.…”

Section: ( )mentioning

confidence: 99%

“…This can be made precise in terms of a metric [18], although there are other equivalent ways to do so, e.g., in terms of covers in compact Hausdorff spaces [19]. The topological entropy is a way of counting the number of distinct trajectories which are generated as the dynamical system evolves in time 11 . For a dynamical system governed by a given iterated function, the topological entropy can be thought of as a measure of the exponential growth rate of the number of distinguishable orbits, which is an extended real number.…”

Section: Topological Entropymentioning

confidence: 99%

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Topological theory of physical fields

Jafari

Vishniac

2020

J. Phys. Commun.

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We study the topology associated with physical vector and scalar fields. A mathematical object, e.g., a ball, can be continuously deformed, without tearing or gluing, to make other topologically equivalent objects, e.g., a cube or a solid disk. If tearing or gluing get involved, i.e. the deformation is not continuous anymore, the initial topology will consequently change giving rise to a topologically distinct object, e.g., a torus. This simple concept in general topology may be employed in the study of physical systems described by fields. Instead of continuously deforming objects, we can take a continuously evolving field, with an appropriately defined topology, such that the topology remains unchanged in time unless the system undergoes an important physical change, e.g., a transition to a different energy state. For instance, a sudden change in the magnetic topology in an energetically relaxing plasma, a process called reconnection, strongly affects the dynamics, e.g., it is involved in launching solar flares and generating large scale magnetic fields in astrophysical objects. In this topological formalism, the magnetic topology in a plasma can spontaneously change due to the presence of dissipative terms in the induction equation which break its time symmetry. We define a topology for the vector field F in the phase space ( ) F x, . As for scalar fields represented by a perfect fluid, e.g., the inhomogeneous inflaton or Higgs fields, the fluid velocity u defines the corresponding topology. The vector field topology in its corresponding phase space ( ) F x, will be preserved in time if certain conditions including time reversal invariance are satisfied by the field and its governing differential equation. Otherwise, the field's topology can suddenly change at some point, similar to a spontaneously broken symmetry, as time advances, e.g., corresponding to an energy transition.

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Section: Vector Fieldsmentioning

confidence: 99%

Section: Spatial Complexitymentioning

confidence: 99%

Section: Field Linesmentioning

confidence: 99%

Section: ( )mentioning

confidence: 99%

Section: Topological Entropymentioning

confidence: 99%

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Topological theory of physical fields

Jafari

Vishniac

2020

J. Phys. Commun.

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3D turbulent reconnection: Theory, tests, and astrophysical implications

Lazarían¹,

et al. 2020

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Magnetic reconnection, topological change in magnetic fields, is a fundamental process in magnetized plasmas. It is associated with energy release in regions of magnetic field annihilation, but this is only one facet of this process. Astrophysical fluid flows normally have very large Reynolds numbers and are expected to be turbulent, in agreement with observations. In strong turbulence magnetic field lines constantly reconnect everywhere and on all scales, thus making magnetic reconnection an intrinsic part of the turbulent cascade. We note in particular that this is inconsistent with the usual practice of regarding magnetic field lines as persistent dynamical elements. A number of theoretical, numerical, and observational studies starting with the Lazarian & Vishniac 1999 paper proposed that 3D turbulence makes magnetic reconnection fast and that magnetic reconnection and turbulence are intrinsically connected. In particular, we discuss the dramatic violation of the textbook concept of magnetic flux-freezing in the presence of turbulence. We demonstrate that in the presence of turbulence the plasma effects are subdominant to turbulence as far as the magnetic reconnection is concerned. The latter fact justifies an MHD-like treatment of magnetic reconnection on all scales much larger than the relevant plasma scales. We discuss numerical and observational evidence supporting the turbulent reconnection model. In particular, we demonstrate that the tearing reconnection is suppressed in 3D and, unlike the 2D settings, 3D reconnection induces turbulence that makes magnetic reconnection independent of resistivity. We show that turbulent reconnection dramatically affects key astrophysical processes, e.g. star formation, turbulent dynamo, acceleration of cosmic rays. We provide criticism of the concept of "reconnection-mediated turbulence" and explain why turbulent reconnection is very different from enhanced turbulent resistivity and hyper-resistivity, and why the latter have fatal conceptual flaws.

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Turbulent drag reduction in magnetohydrodynamic and quasi-static magnetohydrodynamic turbulence

2020

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In hydrodynamic turbulence, the kinetic energy injected at large scales cascades to the inertial range, leading to a constant kinetic energy flux. In contrast, in magnetohydrodynamic (MHD) turbulence, a fraction of kinetic energy is transferred to the magnetic energy. Consequently, for the same kinetic energy injection rate, the kinetic energy flux in MHD turbulence is reduced compared to its hydrodynamic counterpart. This leads to relative weakening of the nonlinear term ⟨|(u·∇)u|⟩, (where u is the velocity field) and turbulent drag, but strengthening of the velocity field in MHD turbulence. We verify the above using shell model simulations of hydrodynamic and MHD turbulence. Quasi-static MHD turbulence too exhibits turbulent drag reduction similar to MHD turbulence.

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Topology and stochasticity of turbulent magnetic fields

Cited by 15 publications

References 30 publications

Topological theory of physical fields

Topological theory of physical fields

3D turbulent reconnection: Theory, tests, and astrophysical implications

Turbulent drag reduction in magnetohydrodynamic and quasi-static magnetohydrodynamic turbulence

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