Large-scale magnetic fields at high Reynolds numbers in magnetohydrodynamic simulations

Hotta, Hideyuki; Rempel, Matthias; Yokoyama, T.

doi:10.1126/science.aad1893

Cited by 113 publications

(138 citation statements)

References 25 publications

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“…Our results appear to stand apart from similar studies in full spherical shells (e.g., Nelson et al 2013;Hotta et al 2016) in that the differential rotation is strongly quenched as a function of the magnetic Reynolds number. However, in Nelson et al (2013) the values of Rm (=2πRe M ) correspond to a range of 8 .…”

Section: Differential Rotation and Meridional Circulationcontrasting

confidence: 99%

“…This is roughly consistent with our results. On the other hand, Hotta et al (2016) reached higher values of Re M than in the present study, but no strong quenching was reported. The reason might be that their models are rotating substantially slower than ours, leading to weaker magnetic fields and a weaker back-reaction to the flow.…”

Section: Differential Rotation and Meridional Circulationcontrasting

confidence: 89%

“…We emphasize that this applies to simulations of all groups, although the nomenclature may be different (see Table A.1). This is also true for groups using realistic luminosities, and thus the correct order of magnitude for the radiative diffusivity (e.g., Brun et al 2004;Hotta et al 2016).…”

Section: Introductionmentioning

confidence: 89%

“…An illuminating example is the study of Nelson et al (2013), where the large-scale axisymmetric field decreases by a factor of two when the magnetic Reynolds number is increased by a factor of four, which is still rather steep. In a recent paper, Hotta et al (2016) showed that in even higher-Re M simulations the mean magnetic energy recovers, and the authors claim that this is a consequence of an efficient small-scale dynamo that suppresses small-scale flows. Another goal of the present paper is therefore to study the saturation level of the large-scale field in convection-driven dynamos in spherical coordinates with and without a simultaneous smallscale dynamo (hereafter SSD).…”

Section: Introductionmentioning

confidence: 99%

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Convection-driven spherical shell dynamos at varying Prandtl numbers

Käpylä

Olspert

et al. 2017

A&A

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Context. Stellar convection zones are characterized by vigorous high-Reynolds number turbulence at low Prandtl numbers. Aims. We study the dynamo and differential rotation regimes at varying levels of viscous, thermal, and magnetic diffusion. Methods. We perform three-dimensional simulations of stratified fully compressible magnetohydrodynamic convection in rotating spherical wedges at various thermal and magnetic Prandtl numbers (from 0.25 to 2 and from 0.25 to 5, respectively). Differential rotation and large-scale magnetic fields are produced self-consistently. Results. We find that for high thermal diffusivity, the rotation profiles show a monotonically increasing angular velocity from the bottom of the convection zone to the top and from the poles toward the equator. For sufficiently rapid rotation, a region of negative radial shear develops at mid-latitudes as the thermal diffusivity is decreased, corresponding to an increase of the Prandtl number. This coincides with and results in a change of the dynamo mode from poleward propagating activity belts to equatorward propagating ones. Furthermore, the clearly cyclic solutions disappear at the highest magnetic Reynolds numbers and give way to irregular sign changes or quasi-stationary states. The total (mean and fluctuating) magnetic energy increases as a function of the magnetic Reynolds number in the range studied here (5-151), but the energies of the mean magnetic fields level off at high magnetic Reynolds numbers. The differential rotation is strongly affected by the magnetic fields and almost vanishes at the highest magnetic Reynolds numbers. In some of our most turbulent cases, however, we find that two regimes are possible, where either differential rotation is strong and mean magnetic fields are relatively weak, or vice versa. Conclusions. Our simulations indicate a strong nonlinear feedback of magnetic fields on differential rotation, leading to qualitative changes in the behaviors of large-scale dynamos at high magnetic Reynolds numbers. Furthermore, we do not find indications of the simulations approaching an asymptotic regime where the results would be independent of diffusion coefficients in the parameter range studied here.

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Section: Differential Rotation and Meridional Circulationcontrasting

confidence: 99%

Section: Differential Rotation and Meridional Circulationcontrasting

confidence: 89%

Section: Introductionmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

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Convection-driven spherical shell dynamos at varying Prandtl numbers

Käpylä

Olspert

et al. 2017

A&A

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“…Thus the natural way of studying the solar dynamo is by solving the basic magnetohydrodynamic (MHD) equations in a rotating spherical shell, encompassing the SCZ. However, though substantial progress has been made in recent years in studying fundamental dynamo mechanisms (e.g., Charbonneau 2014; Augustson et al 2015;Featherstone & Miesch 2015;Hotta et al 2016;Käpylä et al 2016;, MHD simulations still cannot capture all processes relevant to the solar dynamo and the solar cycle (Fan & Fang 2014;Karak et al 2015). One reason could be that these simulations do not produce sufficient flux emergence in the form of tilted bipolar magnetic regions (BMRs) that we see in the solar observations (e.g., Wang & Sheeley 1989).…”

Section: Introductionmentioning

confidence: 93%

Solar Cycle Variability Induced by Tilt Angle Scatter in a Babcock–Leighton Solar Dynamo Model

Karak

Miesch

2017

ApJ

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We present results from a three-dimensional Babcock-Leighton dynamo model that is sustained by the explicit emergence and dispersal of bipolar magnetic regions (BMRs). On average, each BMR has a systematic tilt given by Joy's law. Randomness and nonlinearity in the BMR emergence of our model produce variable magnetic cycles. However, when we allow for a random scatter in the tilt angle to mimic the observed departures from Joy's law, we find more variability in the magnetic cycles. We find that the observed standard deviation in Joy's law of σ δ = 15• produces a variability comparable to observed solar cycle variability of ∼ 32%, as quantified by the sunspot number maxima between 1755-2008. We also find that tilt angle scatter can promote grand minima and grand maxima. The time spent in grand minima for σ δ = 15• is somewhat less than that inferred for the Sun from cosmogenic isotopes (about 9% compared to 17%). However, when we double the tilt scatter to σ δ = 30• , the simulation statistics are comparable to the Sun (∼18% of the time in grand minima and ∼ 10% in grand maxima). Though the Babcock-Leighton mechanism is the only source of poloidal field, we find that our simulations always maintain magnetic cycles even at large fluctuations in the tilt angle. We also demonstrate that tilt quenching is a viable and efficient mechanism for dynamo saturation; a suppression of the tilt by only 1-2• is sufficient to limit the dynamo growth. Thus, any potential observational signatures of tilt quenching in the Sun may be subtle.

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Performance benchmarks for a next generation numerical dynamo model

Matsui

Heien

Aubert

et al. 2016

Geochem. Geophys. Geosyst.

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Abstract.Numerical simulations of the geodynamo have successfully represented many observable characteristics of the geomagnetic field, yielding insight into the fundamental processes that generate magnetic fields in the Earth's core. Because of limited spatial resolution, however, the diffusivities in numerical dynamo models are much larger than those in the Earth's core, and consequently, questions remain about how realistic these models are. The typical strategy used to address this issue has been to continue to increase the resolution of these quasi-laminar models with increasing computational resources, thus pushing them toward more realistic parameter regimes. We assess which methods are most promising for the next generation of supercomputers, which will offer access to O(10 6 ) processor cores for large problems. Here we report performance and accuracy benchmarks from 15 dynamo codes that employ a range of numerical and parallelization methods. Computational performance is assessed on the basis of weak and strong scaling behavior up to 16,384 processor cores. Extrapolations of our weak scaling results indicate that dynamo codes that employ two-or three-dimensional domain decompositions can perform efficiently on up to ∼ 10 6 processor cores, paving the way for more realistic simulations in the next model generation.

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Large-scale magnetic fields at high Reynolds numbers in magnetohydrodynamic simulations

Cited by 113 publications

References 25 publications

Convection-driven spherical shell dynamos at varying Prandtl numbers

Convection-driven spherical shell dynamos at varying Prandtl numbers

Solar Cycle Variability Induced by Tilt Angle Scatter in a Babcock–Leighton Solar Dynamo Model

Performance benchmarks for a next generation numerical dynamo model

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