Global dynamo models from direct numerical simulations and their mean-field counterparts

Schrinner, M.

doi:10.1051/0004-6361/201116642

Cited by 50 publications

(29 citation statements)

References 29 publications

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“…We also include the nonlinear generation effects which is induced by the large-scale current and the global rotation that is usually called as the Ω × J effect or the δ dynamo effect (Rädler 1969). It is supported by the numerical simulations (Käpylä et al 2008;Schrinner 2011). P08 suggested that:…”

Section: Appendixmentioning

confidence: 71%

The origin of the helicity hemispheric sign rule reversals in the mean-field solar-type dynamo

Пипин¹,

Zhang²,

Sokoloff³

et al. 2013

Monthly Notices of the Royal Astronomical Society

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Observations of proxies of the magnetic helicity in the Sun over the past two solar cycles revealed reversals of the helicity hemispheric sign rule (negative in the North and positive in the South hemispheres). We apply the mean-field solar dynamo model to study the reversals of the magnetic helicity sign for the dynamo operating in the bulk of the solar convection zone. The evolution of the magnetic helicity is governed by the conservation law. We found that the reversal of the sign of the small-scale magnetic helicity follows the dynamo wave propagating inside the convection zone. Therefore, the spatial patterns of the magnetic helicity reversals reflect the processes which contribute to generation and evolution of the large-scale magnetic fields. At the surface the patterns of the helicity sign reversals are determined by the magnetic helicity boundary conditions at the top of the convection zone. We demonstrate the impact of fluctuations in the dynamo parameters and variability in dynamo cycle amplitude on the reversals of the magnetic helicity sign rule. The obtained results suggest that the magnetic helicity of the large-scale axisymmetric field can be treated as an additional observational tracer for the solar dynamo.

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Section: Appendixmentioning

confidence: 71%

The origin of the helicity hemispheric sign rule reversals in the mean-field solar-type dynamo

Пипин¹,

Zhang²,

Sokoloff³

et al. 2013

Monthly Notices of the Royal Astronomical Society

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“…Whereas Yadav et al (2013b) obtained very similar scaling laws for models with variable conductivities, Duarte et al (2013) reported that the field topology of some models depends on the radial conductivity profile. A mean-field analysis (Schrinner et al 2007;Schrinner 2011) of numerical dynamo models in the anelastic approximation might give more detailed insight in relevant dynamo processes and is envisaged for a future study. M.…”

Section: Discussionmentioning

confidence: 99%

Topology and field strength in spherical, anelastic dynamo simulations

Schrinner

Petitdemange

Raynaud

et al. 2014

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Context. Numerical modelling of convection driven dynamos in the Boussinesq approximation revealed fundamental characteristics of the dynamo-generated magnetic fields and the fluid flow. Because these results were obtained for an incompressible fluid of constant density, their validity for gas planets and stars remains to be assessed. A common approach is to take some density stratification into account with the so-called anelastic approximation.Aims. The validity of previous results obtained in the Boussinesq approximation is tested for anelastic models. We point out and explain specific differences between both types of models, in particular, with respect to the field geometry and the field strength, but we also compare scaling laws for the velocity amplitude, the magnetic dissipation time, and the convective heat flux. Methods. Our investigation is based on a systematic parameter study of spherical dynamo models in the anelastic approximation. We make use of a recently developed numerical solver and provide results for the test cases of the anelastic dynamo benchmark. Results. The dichotomy of dipolar and multipolar dynamos identified in Boussinesq simulations is also present in our sample of anelastic models. Dipolar models require that the typical length scale of convection is an order of magnitude larger than the Rossby radius. However, the distinction between both classes of models is somewhat less explicit than in previous studies. This is mainly due to two reasons: we found a number of models with a considerable equatorial dipole contribution and an intermediate overall dipole field strength. Furthermore, a large density stratification may hamper the generation of dipole dominated magnetic fields. Previously proposed scaling laws, such as those for the field strength, are similarly applicable to anelastic models. It is not clear, however, if this consistency necessarily implies similar dynamo processes in both settings.

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“…For the poloidal field, we apply a condition of smooth transition from the internal poloidal field to the external potential (vacuum) field. Summing up, the model includes magnetic field generation effects due to the differential rotation (Ω-effect), turbulent kinetic helicity (the anisotropic α-effect) and interaction of largescale currents with the global rotation, usually called Ω × Jeffect or δ-effect (Rädler 1969;Käpylä et al 2008;Schrinner 2011). For the differential rotation, we use an analytical fit to the recent helioseismology results of Howe et al (2011;see mean density and turbulent intensity gradients (so-called "gradient pumping").…”

Section: Solar Dynamo Model With Subsurface Shearmentioning

confidence: 99%

Effects of Anisotropies in Turbulent Magnetic Diffusion in Mean-Field Solar Dynamo Models

Пипин

Kosovichev

2014

ApJ

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We study how anisotropies of turbulent diffusion affect the evolution of large-scale magnetic fields and the dynamo process on the Sun. The effect of anisotropy is calculated in a mean-field magnetohydrodynamics framework assuming that triple correlations provide relaxation to the turbulent electromotive force (so-called the "minimal τ -approximation"). We examine two types of mean-field dynamo models: the well-known benchmark flux-transport model and a distributed-dynamo model with a subsurface rotational shear layer. For both models, we investigate effects of the double-and triple-cell meridional circulation, recently suggested by helioseismology and numerical simulations. To characterize the anisotropy effects, we introduce a parameter of anisotropy as a ratio of the radial and horizontal intensities of turbulent mixing. It is found that the anisotropy affects the distribution of magnetic fields inside the convection zone. The concentration of the magnetic flux near the bottom and top boundaries of the convection zone is greater when the anisotropy is stronger. It is shown that the critical dynamo number and the dynamo period approach to constant values for large values of the anisotropy parameter. The anisotropy reduces the overlap of toroidal magnetic fields generated in subsequent dynamo cycles, in the time-latitude "butterfly" diagram. If we assume that sunspots are formed in the vicinity of the subsurface shear layer, then the distributed dynamo model with the anisotropic diffusivity satisfies the observational constraints from helioseismology and is consistent with the value of effective turbulent diffusion estimated from the dynamics of surface magnetic fields.

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Global dynamo models from direct numerical simulations and their mean-field counterparts

Cited by 50 publications

References 29 publications

The origin of the helicity hemispheric sign rule reversals in the mean-field solar-type dynamo

The origin of the helicity hemispheric sign rule reversals in the mean-field solar-type dynamo

Topology and field strength in spherical, anelastic dynamo simulations

Effects of Anisotropies in Turbulent Magnetic Diffusion in Mean-Field Solar Dynamo Models

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