MHD Dynamos and Turbulence

Tobias, Steven M.; Cattaneo, Fausto; Boldyrev, Stanislav

doi:10.1017/cbo9781139032810.010

Cited by 53 publications

(71 citation statements)

References 125 publications

(158 reference statements)

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“…1 and 2 that the compensated energy spectra show a flat region that extends as the Reynolds number is increased. This is consistent with previous, lower resolution simulations of strongly magnetized MHD turbulence (see, e.g., [16,48,[51][52][53][54][55][56]). In the imbalanced case, the interpretation of the numerical results is not as straightforward.…”

Section: Discussionsupporting

confidence: 93%

“…Most of the conclusions of those papers appear to be at odds with ours (and with similar results or other groups, e.g., [16,48,[51][52][53][54][55][56]). We, however, note that the actual numerical results presented in [57][58][59] agree with ours in the range of scales that we study, while they differ from ours at very large wave numbers, e.g., k * 50 in the runs with highest resolution.…”

Section: à3=2 ?contrasting

confidence: 50%

“…These statements, in our opinion, are not supported by the factual numerical data presented in these papers. Until the effects of hyperdissipation are better understood and numerical convergence is demonstrated in the settings of [57][58][59], it is hard to assess fully the degree to which the numerical findings of [57][58][59] can be compared with our results, or with similar results of other groups (see, e.g., [16,48,[51][52][53][54][55][56] . In these runs, the numerical discretization is not related to the dissipation scale as N ?…”

Section: à3=2 ?mentioning

confidence: 88%

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On the Energy Spectrum of Strong Magnetohydrodynamic Turbulence

et al. 2012

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The energy spectrum of magnetohydrodynamic turbulence attracts interest due to its fundamental importance and its relevance for interpreting astrophysical data. Here we present measurements of the energy spectra from a series of high-resolution direct numerical simulations of magnetohydrodynamics turbulence with a strong guide field and for increasing Reynolds number. The presented simulations, with numerical resolutions up to 2048 3 mesh points and statistics accumulated over 30 to 150 eddy turnover times, constitute, to the best of our knowledge, the largest statistical sample of steady state magnetohydrodynamics turbulence to date. We study both the balanced case, where the energies associated with Alfvén modes propagating in opposite directions along the guide field, E þ ðk ? Þ and E À ðk ? Þ, are equal, and the imbalanced case where the energies are different. In the balanced case, we find that the energy spectrum converges to a power law with exponent À3=2 as the Reynolds number is increased, which is consistent with phenomenological models that include scale-dependent dynamic alignment. For the imbalanced case, withfor all Reynolds numbers considered, while E þ has a slightly steeper spectrum at small Re. As the Reynolds number increases, E þ flattens. Since E AE are pinned at the dissipation scale and anchored at the driving scales, we postulate that at sufficiently high Re the spectra will become parallel in the inertial range and scale as E þ / E À / k À3=2 ?. Questions regarding the universality of the spectrum and the value of the ''Kolmogorov constant'' are discussed.

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Section: Discussionsupporting

confidence: 93%

Section: à3=2 ?contrasting

confidence: 50%

Section: à3=2 ?mentioning

confidence: 88%

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On the Energy Spectrum of Strong Magnetohydrodynamic Turbulence

et al. 2012

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“…It is useful to discuss the conservation laws of Equations (1)-(2). In the non-rotating system, the MHD equations conserve the quadratic integrals of energy, cross helicity, and magnetic helicity if the external energy supply and energy dissipation are absent (e.g., Biskamp 2003;Tobias et al 2011). In the MRI case, energy is injected into the system by the instability.…”

Section: Numerical Setupmentioning

confidence: 99%

Magnetorotational dynamo action in the shearing box

Walker

Boldyrev

2017

Monthly Notices of the Royal Astronomical Society

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Magnetic dynamo action caused by the magnetorotational instability is studied in the shearing-box approximation with no imposed net magnetic flux. Consistent with recent studies, the dynamo action is found to be sensitive to the aspect ratio of the box: it is much easier to obtain in tall boxes (stretched in the direction normal to the disk plane) than in long boxes (stretched in the radial direction). Our direct numerical simulations indicate that the dynamo is possible in both cases, given a large enough magnetic Reynolds number. To explain the relatively larger effort required to obtain the dynamo action in a long box, we propose that the turbulent eddies caused by the instability most efficiently fold and mix the magnetic field lines in the radial direction. As a result, in the long box the scale of the generated strong azimuthal (stream-wise directed) magnetic field is always comparable to the scale of the turbulent eddies. In contrast, in the tall box the azimuthal magnetic flux spreads in the vertical direction over a distance exceeding the scale of the turbulent eddies. As a result, different vertical sections of the tall box are permeated by large-scale nonzero azimuthal magnetic fluxes, facilitating the instability. In agreement with this picture, the cases when the dynamo is efficient are characterized by a strong intermittency of the local azimuthal magnetic fluxes.

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“…Following the seminal work of Kazantsev (1967), there has been considerable interest in fluctuation dynamos, in terms of theoretical developments, in terms of their direct simulation and in terms of various astrophysical applications (Molchanov et al 1985;Zeldovich et al 1990;Kulsrud & Anderson 1992;Subramanian 1997;Rogachevskii & Kleeorin 1997;Subramanian 1999;Chertkov et al 1999;Haugen et al 2004;Schekochihin et al 2004Schekochihin et al , 2005Brandenburg & Subramanian 2005;Subramanian et al 2006;Enßlin & Vogt 2006;Cho et al 2009;Malyshkin & Boldyrev 2010;Federrath et al 2011;Tobias et al 2011;Sur et al 2012;Schober et al 2012;Beresnyak 2012;Brandenburg et al 2012;Bhat & Subramanian 2013). These works have clearly demonstrated that random (or turbulent) flows in a conducting plasma, with R M > R crit ∼ 30 − 500, leads to the amplification of magnetic fields on the fast eddy turn over time scale, usually much smaller than the age of the astrophysical system.…”

Section: Introductionmentioning

confidence: 99%

Fluctuation dynamos at finite correlation times using renewing flows

Bhat

Subramanian

2015

J. Plasma Phys.

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Fluctuation dynamos are generic to turbulent astrophysical systems. The only analytical model of the fluctuation dynamo, due to Kazantsev, assumes the velocity to be deltacorrelated in time. This assumption breaks down for any realistic turbulent flow. We generalize the analytic model of fluctuation dynamo to include the effects of a finite correlation time, τ , using renewing flows. The generalized evolution equation for the longitudinal correlation function M L leads to the standard Kazantsev equation in the τ → 0 limit, and extends it to the next order in τ . We find that this evolution equation involves also third and fourth spatial derivatives of M L , indicating that the evolution for finite τ will be non-local in general. In the perturbative case of small-τ (or small Strouhl number), it can be recast using the Landau-Lifschitz approach, to one with at most second derivatives of M L . Using both a scaling solution and the WKBJ approximation, we show that the dynamo growth rate is reduced when the correlation time is finite. Interestingly, to leading order in τ , we show that the magnetic power spectrum, preserves the Kazantsev form, M (k) ∝ k 3/2 , in the large k limit, independent of τ .

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MHD Dynamos and Turbulence

Cited by 53 publications

References 125 publications

On the Energy Spectrum of Strong Magnetohydrodynamic Turbulence

On the Energy Spectrum of Strong Magnetohydrodynamic Turbulence

Magnetorotational dynamo action in the shearing box

Fluctuation dynamos at finite correlation times using renewing flows

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