Direct Evidence of the Transition from Weak to Strong Magnetohydrodynamic Turbulence

Meyrand, Romain; Galtier, Sébastien; Kiyani, K. H.

doi:10.1103/physrevlett.116.105002

Cited by 57 publications

(70 citation statements)

References 42 publications

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“…[18] for example. It was reported in magnetohydrodynamic turbulence that the wave numbers at which the ratio of the nonlinear time scale to the linear time scale χ k = 1/3 are the critical wave numbers separating the weak and strong turbulence [27]. Note that the value 1/3 is introduced as a rough indication because the transition between the wave-dominant range and the vortex-dominant range is gradual.…”

Section: B Distribution Of Turbulence Indices In Wave-number Spacementioning

confidence: 99%

“…The anisotropy of the time scales can be introduced by using the period given by the linear dispersion relation instead of the Brunt-Väisälä period as the linear time scale [24]. The wave number at which the period given by the linear dispersion relation and the eddy-turnover time are comparable can separate the weak-wave turbulence and the isotropic or anisotropic strong turbulence in magnetohydrodynamic turbulence [17,[25][26][27]. However, it is not clear in rotating turbulence [28].…”

Section: Introductionmentioning

confidence: 99%

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Energy-based analysis and anisotropic spectral distribution of internal gravity waves in strongly stratified turbulence

Yokoyama

Takaoka

2019

Phys. Rev. Fluids

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Stratified turbulence shows scale-and direction-dependent anisotropy and the coexistence of weak turbulence of internal gravity waves and strong turbulence of eddies. Straightforward application of standard analyses developed in isotropic turbulence sometimes masks important aspects of the anisotropic turbulence. To capture detailed structures of the energy distribution in the wave-number space, it is indispensable to examine the energy distribution with non-integrated spectra by fixing the codimensional wave-number component or in the two-dimensional domain spanned by both the horizontal and vertical wave numbers. Indices which separate the range of the anisotropic weak-wave turbulence in the wave-number space are proposed based on the decomposed energies. In addition, the dominance of the waves in the range is also verified by the small frequency deviation from the linear dispersion relation. In the wave-dominant range, the linear wave periods given by the linear dispersion relation are smaller than approximately one third of the eddy-turnover time. The linear wave periods reflect the anisotropy of the system, while the isotropic Brunt-Väisälä period is used to evaluate the Ozmidov wave number, which is necessarily isotropic. It is found that the time scales in consideration of the anisotropy of the flow field must be appropriately selected to obtain the critical wave number separating the weak-wave turbulence. *

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Section: B Distribution Of Turbulence Indices In Wave-number Spacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Energy-based analysis and anisotropic spectral distribution of internal gravity waves in strongly stratified turbulence

Yokoyama

Takaoka

2019

Phys. Rev. Fluids

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“…Whether the radial axis stops to rule the anisotropy at small scales depends on the tendency of turbulence to become strong, in analogy to the switch from weak to strong turbulence in homogenous MHD (e.g. Verdini & Grappin 2012;Meyrand et al 2016). For the solar wind, it is still unclear whether axisymmetry around the mean field is restored at proton scales (Hamilton et al 2008;Narita et al 2010;Roberts et al 2017;Lacombe et al 2017).…”

mentioning

confidence: 99%

Three-dimensional local anisotropy of velocity fluctuations in the solar wind

Verdini

Grappin

Alexandrova

et al. 2019

Monthly Notices of the Royal Astronomical Society

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We analyse velocity fluctuations in the solar wind at magneto-fluid scales in two datasets, extracted from Wind data in the period 2005-2015, that are characterised by strong or weak expansion. Expansion affects measurements of anisotropy because it breaks axisymmetry around the mean magnetic field. Indeed, the small-scale threedimensional local anisotropy of magnetic fluctuations (δB) as measured by structure functions (SF B ) is consistent with tube-like structures for strong expansion. When passing to weak expansion, structures become ribbon-like because of the flattening of SF B along one of the two perpendicular directions. The power-law index that is consistent with a spectral slope −5/3 for strong expansion now becomes closer to −3/2. This index is also characteristic of velocity fluctuations in the solar wind. We study velocity fluctuations (δV) to understand if the anisotropy of their structure functions (SF V ) also changes with the strength of expansion and if the difference with the magnetic spectral index is washed out once anisotropy is accounted for. We find that SF V is generally flatter than SF B . When expansion passes from strong to weak, a further flattening of the perpendicular SF V occurs and the small-scale anisotropy switches from tube-like to ribbon-like structures. These two types of anisotropy, common to SF V and SF B , are associated to distinct large-scale variance anisotropies of δB in the strong-and weak-expansion datasets. We conclude that SF V show anisotropic threedimensional scaling similar to SF B , with however systematic flatter scalings, reflecting the difference between global spectral slopes.

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“…Both χ u and χ b grow as k ⊥ increases and so there will be some scale (provided that dissipation is weak enough) at which the WWT assumption is broken and where the CB assumption becomes relevant. Such a transition from weak to strong wave turbulence has been observed in numerical simulations of Alfvén wave turbulence (Meyrand et al 2016) and Hall MHD turbulence (Meyrand et al 2017).…”

Section: Domain Of Validity For Weak Wave Turbulence Approachmentioning

confidence: 60%

Rotating magnetohydrodynamic turbulence

Bell¹,

Nazarenko²

2019

J. Phys. A: Math. Theor.

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Turbulence in rotating Magneto-hydrodynamic systems is studied theoretically and numerically. In the linear limit, when the velocity and magnetic perturbations are small, the system supports two types of waves. When the rotation effects are stronger than the ones of the external magnetic field, one of these waves contains most of the kinetic energy (inertial wave) and the other -most of the magnetic energy (magnetostrophic wave). The weak wave turbulence (WWT) theory for decoupled inertial and magnetospheric wave systems was previously derived by Galtier (2014). In the present paper, we derive theory of strong turbulence for such waves based on the critical balance (CB) approach conjecturing that the linear and nonlinear timescales are of similar magnitudes in a wide range of turbulent scales. Regimes of weak and strong wave turbulence are simulated numerically. The results appear to be in good agreement with the WWT and CB predictions, particularly for the exponents of the kinetic and magnetic energy spectra.

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Direct Evidence of the Transition from Weak to Strong Magnetohydrodynamic Turbulence

Cited by 57 publications

References 42 publications

Energy-based analysis and anisotropic spectral distribution of internal gravity waves in strongly stratified turbulence

Energy-based analysis and anisotropic spectral distribution of internal gravity waves in strongly stratified turbulence

Three-dimensional local anisotropy of velocity fluctuations in the solar wind

Rotating magnetohydrodynamic turbulence

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