Weak turbulence in two-dimensional magnetohydrodynamics

Tronko, Natalia; Nazarenko, Sergey; Galtier, Sébastien

doi:10.1103/physreve.87.033103

Cited by 16 publications

(15 citation statements)

References 57 publications

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“…The transition to the new spectral scaling, however, was not observed in these studies. Although the 2D case is qualitatively different from its 3D counterpart [32,59], these numerical results may also be explained by insufficiently large S L numbers, or they may, possibly, indicate our incomplete understanding of the reconnection-dominated interval. Indeed, the scaling (18) and the spectrum (19) are phenomenological estimates in that they have not been self-consistently derived from a theory of a reconnection-dominated cascade.…”

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confidence: 81%

Role of Magnetic Reconnection in Magnetohydrodynamic Turbulence

2017

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The current understanding of magnetohydrodynamic (MHD) turbulence envisions turbulent eddies which are anisotropic in all three directions. In the plane perpendicular to the local mean magnetic field, this implies that such eddies become current-sheetlike structures at small scales. We analyze the role of magnetic reconnection in these structures and conclude that reconnection becomes important at a scale, where S L is the outer-scale (L) Lundquist number and λ is the smallest of the fieldperpendicular eddy dimensions. This scale is larger than the scale set by the resistive diffusion of eddies, therefore implying a fundamentally different route to energy dissipation than that predicted by the Kolmogorov-like phenomenology. In particular, our analysis predicts the existence of the subinertial, reconnection interval of MHD turbulence, with the estimated scaling of the Fourier energy spectrum⊥ , where k ⊥ is the wave number perpendicular to the local mean magnetic field. The same calculation is also performed for high (perpendicular) magnetic Prandtl number plasmas (Pm), where the reconnection scale is found to be λ=L ∼ S Introduction.-Turbulence is a defining feature of magnetized plasmas in space and astrophysical environments, which are almost invariably characterized by very large Reynolds numbers. The solar wind [1], the interstellar medium [2,3], and accretion disks [4,5] are prominent examples of plasmas dominated by turbulence, where its detailed understanding is almost certainly key to addressing long-standing puzzles such as electron-ion energy partition, cosmic ray acceleration, magnetic dynamo action, and momentum transport.Weak collisionality implies that kinetic plasma physics is required to fully describe turbulence in many such environments [6]. However, turbulent motions at scales ranging from the system size to the ion kinetic scales, an interval which spans many orders of magnitude, should be accurately described by magnetohydrodynamics (MHD).The current theoretical understanding of MHD turbulence largely rests on the ideas that were put forth by Kolmogorov and others to describe turbulence in neutral fluids (the K41 theory of turbulence [7]), and then adapted to magnetized plasmas by Iroshnikov and Kraichnan [8,9] and, later, Goldreich and Sridhar (GS95) [10]. Very briefly, one considers energy injection at some large scale L (the forcing, or outer, scale), which then cascades to smaller scales through the inertial range where, by definition, dissipation is negligible and throughout which, therefore, energy is conserved. At the bottom of the cascade is the dissipation range, where the gradients in the flow are sufficiently large for the dissipation to be efficient.Turbulence in magnetized plasmas fundamentally differs from that in neutral fluids due to the intrinsic anisotropy

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confidence: 81%

Role of Magnetic Reconnection in Magnetohydrodynamic Turbulence

2017

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“…In particular, this intuition may be useful in the attempt to incorporate the role of the k = 0 modes into a refined theory. 79 An important property of plasma turbulence that is highlighted by the solution obtained here is the inherently three-dimensional nature of turbulence in a magnetized plasma 65,80 , as discussed in §II D. Motivated by the power arising at k ≈ 0 in MHD turbulence simulations, 81,82 to achieve higher spatial resolution, many recent studies of plasma turbulence have employed two-dimensional simulations in the plane perpendicular to the mean magnetic field. [83][84][85][86][87][88][89][90][91] However, these 2D simulations cannot describe the dynamics of Alfvén waves, which are generally considered to be fundamental to the turbulence.…”

Section: Implications For Turbulence In Astrophysical Plasmasmentioning

confidence: 94%

Alfvén wave collisions, the fundamental building block of plasma turbulence. I. Asymptotic solution

2013

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The nonlinear interaction between counterpropagating Alfvén waves is the physical mechanism underlying the cascade of energy to small scales in astrophysical plasma turbulence. Beginning with the equations for incompressible MHD, an asymptotic analytical solution for the nonlinear evolution of these Alfvén wave collisions is derived in the weakly nonlinear limit. The resulting qualitative picture of nonlinear energy transfer due to this mechanism involves two steps: first, the primary counterpropagating Alfvén waves interact to generate an inherently nonlinear, purely magnetic secondary fluctuation with no parallel variation; second, the two primary waves each interact with this secondary fluctuation to transfer energy secularly to two tertiary Alfvén waves. These tertiary modes are linear Alfvén waves with the same parallel wavenumber as the primary waves, indicating the lack of a parallel cascade. The amplitude of these tertiary modes increases linearly with time due to the coherent nature of the resonant four-wave interaction responsible for the nonlinear energy transfer. The implications of this analytical solution for turbulence in astrophysical plasmas is discussed. The solution presented here provides valuable intuition about the nonlinear interactions underlying magnetized plasma turbulence, in support of an experimental program to verify in the laboratory the nature of this fundamental building block of astrophysical plasma turbulence.a)

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“…To derive the wave kinetic equation, one usually starts with the Hamiltonian Equation (24) (although in some cases, it is easier to work with non-Hamiltonian equations, e.g. in MHD turbulence [56,59]). In terms of the waveaction variable a k , the waveaction spectrum is defined as follows,…”

Section: Long-time Statistical Evolution Of Weakly Non-linear Wave Symentioning

confidence: 99%

“…MHD turbulence in the presence of a strong external magnetic field takes the form of Alfvén wave turbulence [56,58,59,[77][78][79][80]. It plays an important role in interstellar and interplanetary media, e.g.…”

Section: Mhd Turbulencementioning

confidence: 99%

Wave turbulence

Nazarenko

2015

Contemporary Physics

289

669

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Wave turbulence is the statistical mechanics of random waves with a broadband spectrum interacting via non-linearity. To understand its difference from non-random well-tuned coherent waves, one could compare the sound of thunder to a piece of classical music. Wave turbulence is surprisingly common and important in a great variety of physical settings, starting with the most familiar ocean waves to waves at quantum scales or to much longer waves in astrophysics. We will provide a basic overview of the wave turbulence ideas, approaches and main results emphasising the physics of the phenomena and using qualitative descriptions avoiding, whenever possible, involved mathematical derivations. In particular, dimensional analysis will be used for obtaining the key scaling solutions in wave turbulence -Kolmogorov-Zakharov (KZ) spectra.

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Weak turbulence in two-dimensional magnetohydrodynamics

Cited by 16 publications

References 57 publications

Role of Magnetic Reconnection in Magnetohydrodynamic Turbulence

Role of Magnetic Reconnection in Magnetohydrodynamic Turbulence

Alfvén wave collisions, the fundamental building block of plasma turbulence. I. Asymptotic solution

Wave turbulence

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