Fully resolved array of simulations investigating the influence of the magnetic Prandtl number on magnetohydrodynamic turbulence

McKay, Mairi; Berera, Arjun; Ho, Richard D. J. G.

doi:10.1103/physreve.99.013101

Cited by 5 publications

(10 citation statements)

References 45 publications

(46 reference statements)

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“…At low and moderate resolutions and for Pm ≤ 10, K /( K + M ) is approximately proportional to Pm 1/3 (dotted line), an empirical scaling reported previously in Refs. [57,58]. For Pm > 10, this ratio becomes roughly independent of Pm at fixed Rm, especially so at our two highest resolutions.…”

Section: E Viscous and Resistive Dissipationmentioning

confidence: 61%

Tearing instability and current-sheet disruption in the turbulent dynamo

Galishnikova¹,

Kunz²,

Schekochihin³

2022

Preprint

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Turbulence in a conducting plasma can amplify seed magnetic fields in what is known as the turbulent, or small-scale, dynamo. The associated growth rate and emergent magnetic-field geometry depend sensitively on the material properties of the plasma, in particular on the Reynolds number Re, the magnetic Reynolds number Rm, and their ratio Pm ≡ Rm/Re. For Pm > 1, the amplified magnetic field is gradually arranged into a folded structure, with direction reversals at the resistive scale and field lines curved at the larger scale of the flow. As the mean magnetic energy grows to come into approximate equipartition with the fluid motions, this folded structure is thought to persist. Using analytical theory and high-resolution MHD simulations with the Athena++ code, we show that these magnetic folds become unstable to tearing during the nonlinear stage of the dynamo for Rm 10 4 and Re 10 3 . An Rm-and Pm-dependent tearing scale, at and below which folds are disrupted, is predicted theoretically and found to match well the characteristic fieldreversal scale measured in the simulations. The disruption of folds by tearing increases the ratio of viscous-to-resistive dissipation. In the saturated state, the magnetic-energy spectrum exhibits a sub-tearing-scale steepening to a slope consistent with that predicted for tearing-mediated Alfvénic turbulence. Its spectral peak appears to be independent of the resistive scale and comparable to the driving scale of the flow, while the magnetic energy resides in a broad range of scales extending down to the field-reversal scale set by tearing. Emergence of a degree of large-scale magnetic coherence in the saturated state of the turbulent dynamo may be consistent with observations of magnetic-field fluctuations in galaxy clusters and recent laboratory experiments.

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Section: E Viscous and Resistive Dissipationmentioning

confidence: 61%

Tearing instability and current-sheet disruption in the turbulent dynamo

Galishnikova¹,

Kunz²,

Schekochihin³

2022

Preprint

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“…In extending findings of Eulerian chaos in hydrodynamics to MHD, there are other complications that must be tested, such as whether λ τ has any dependence on Re or Pr = ν/η, the magnetic Prandtl number. Pr is known to have important effects on dissipation rates and the presence of inverse spectral transfer 35 . This paper relies on this previous foundational work.…”

Section: A Working Hypothesis For λ In Mhdmentioning

confidence: 99%

“…When the magnetic field was forced, A(k) and B(k) were chosen in order to control the magnetic helicity. The necessary benchmarking for the simulations has been done in 35 . This benchmarking included making sure that all simulations were fully resolved in both fields.…”

Section: Direct Numerical Simulationmentioning

confidence: 99%

“…A full table of simulation parameters is shown in Table I. The set of simulations analysed in this section are the same as those used for the main results of 35 . These results may or may not be affected by the onset of dynamo action, but systems showing dynamo action have been shown to be chaotic in the past 41 .…”

Section: A Re and Pr Dependencementioning

confidence: 99%

“…A further discussion on the resolution of these simulations can be found in 35 . The data is publically available online 42 .…”

Section: A Re and Pr Dependencementioning

confidence: 99%

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Chaotic behavior of Eulerian magnetohydrodynamic turbulence

Berera

Clark

2019

Physics of Plasmas

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We study the chaotic properties of a turbulent conducting fluid using direct numerical simulation in the Eulerian frame. The maximal Lyapunov exponent is measured for simulations with varying Reynolds number and magnetic Prandtl number. We extend the Ruelle theory of hydrodynamic turbulence to magnetohydrodynamic turbulence as a working hypothesis and find broad agreement with results. In other simulations we introduce magnetic helicity and these simulations show a diminution of chaos, which is expected to be eliminated at maximum helicity. We also find that the difference between two initially close fields grows linearly at late times, which was also recently found in hydrodynamics. This linear growth rate is found to be dependent on the dissipation rate of the relevant field. We discuss the important consequences this linear growth has on predictability. We infer that the chaos in the system is totally dominated by the velocity field and connect this work to real magnetic systems such as solar weather and confined plasmas.

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MHD turbulence: a biased review

Schekochihin

2022

J. Plasma Phys.

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This review of scaling theories of magnetohydrodynamic (MHD) turbulence aims to put the developments of the last few years in the context of the canonical time line (from Kolmogorov to Iroshnikov–Kraichnan to Goldreich–Sridhar to Boldyrev). It is argued that Beresnyak's (valid) objection that Boldyrev's alignment theory, at least in its original form, violates the Reduced-MHD rescaling symmetry can be reconciled with alignment if the latter is understood as an intermittency effect. Boldyrev's scalings, a version of which is recovered in this interpretation, and the concept of dynamic alignment (equivalently, local 3D anisotropy) are thus an example of a physical theory of intermittency in a turbulent system. The emergence of aligned structures naturally brings into play reconnection physics and thus the theory of MHD turbulence becomes intertwined with the physics of tearing, current-sheet disruption and plasmoid formation. Recent work on these subjects by Loureiro, Mallet et al. is reviewed and it is argued that we may, as a result, finally have a reasonably complete picture of the MHD turbulent cascade (forced, balanced, and in the presence of a strong mean field) all the way to the dissipation scale. This picture appears to reconcile Beresnyak's advocacy of the Kolmogorov scaling of the dissipation cutoff (as $\mathrm {Re}^{3/4}$ ) with Boldyrev's aligned cascade. It turns out also that these ideas open the door to some progress in understanding MHD turbulence without a mean field – MHD dynamo – whose saturated state is argued to be controlled by reconnection and to contain, at small scales, a tearing-mediated cascade similar to its strong-mean-field counterpart (this is a new result). On the margins of this core narrative, standard weak-MHD-turbulence theory is argued to require some adjustment – and a new scheme for such an adjustment is proposed – to take account of the determining part that a spontaneously emergent 2D condensate plays in mediating the Alfvén-wave cascade from a weakly interacting state to a strongly turbulent (critically balanced) one. This completes the picture of the MHD cascade at large scales. A number of outstanding issues are surveyed: imbalanced turbulence (for which a new, tentative theory is proposed), residual energy, MHD turbulence at subviscous scales, and decaying MHD turbulence (where there has been dramatic progress recently, and reconnection again turned out to feature prominently). Finally, it is argued that the natural direction of research is now away from the fluid MHD theory and into kinetic territory – and then, possibly, back again. The review lays no claim to objectivity or completeness, focusing on topics and views that the author finds most appealing at the present moment.

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Fully resolved array of simulations investigating the influence of the magnetic Prandtl number on magnetohydrodynamic turbulence

Abstract: We explore the effect of the magnetic Prandtl number Pm on energy and dissipation in fullyresolved direct numerical simulations of steady-state, mechanically-forced homogeneous magnetohydrodynamic turbulence in the range 1/32 Show more

Cited by 5 publications

References 45 publications

Tearing instability and current-sheet disruption in the turbulent dynamo

Tearing instability and current-sheet disruption in the turbulent dynamo

Chaotic behavior of Eulerian magnetohydrodynamic turbulence

MHD turbulence: a biased review

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