Mean‐field view on rotating magnetoconvection and a geodynamo model

Schrinner, M.; Rädler, K.-H.; Schmitt, D.; Rheinhardt, M.; Christensen, Ulrich R.

doi:10.1002/asna.200410384

Cited by 160 publications

(202 citation statements)

References 5 publications

(7 reference statements)

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“…(22) (Brandenburg & Sokoloff 2002;Kowal et al 2005). A general procedure for determining the full α ij and η ijk tensors from a simulation is to calculate the electromotive force after applying test fields of different directions and with different gradients (Schrinner et al 2005). In the following we adopt xy averages, so the resulting mean fields depend only on z and t, and only B x and B y are non-trivial (B z = 0 because of the solenoidality B).…”

Section: Tensorial Turbulent Resistivitymentioning

confidence: 99%

Turbulence and its parameterization in accretion discs

Brandenburg

2005

Astron Nachr

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Abstract. Accretion disc turbulence is investigated in the framework of the shearing box approximation. The turbulence is either driven by the magneto-rotational instability or, in the non-magnetic case, by an explicit and artificial forcing term in the momentum equation. Unlike the magnetic case, where most of the dissipation occurs in the disc corona, in the forced hydrodynamic case most of the dissipation occurs near the midplane. In the hydrodynamic case evidence is presented for the stochastic excitation of epicycles. When the vertical and radial epicyclic frequencies are different (modeling the properties around rotating black holes), the beat frequency between these two frequencies appear to show up as a peak in the temporal power spectrum in some cases. Finally, the full turbulent resistivity tensor is determined and it is found that, if the turbulence is driven by a forcing term, the signs of its off-diagonal components are such that this effect would not be capable of dynamo action by the shear-current effect.

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Section: Tensorial Turbulent Resistivitymentioning

confidence: 99%

Turbulence and its parameterization in accretion discs

Brandenburg

2005

Astron Nachr

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“…This method is known as the test-field method and was developed by Schrinner et al (2005Schrinner et al ( , 2007 to calculate all tensor components from snapshots of simulations of the geodynamo in a spherical shell. This method was later applied to time-dependent turbulence in triply-periodic Cartesian domains, both with shear and no helicity (Brandenburg 2005 The test-field method has recently been criticized by Cattaneo & Hughes (2008) on the grounds that the test fields are arbitrary pre-determined mean fields.…”

Section: The Test-field Methodsmentioning

confidence: 99%

Advances in Theory and Simulations of Large-Scale Dynamos

Brandenburg

2009

Space Sci Rev

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Recent analytical and computational advances in the theory of large-scale dynamos are reviewed. The importance of the magnetic helicity constraint is apparent even without invoking mean-field theory. The tau approximation yields expressions that show how the magnetic helicity gets incorporated into mean-field theory. The test-field method allows an accurate numerical determination of turbulent transport coefficients in linear and nonlinear regimes. Finally, some critical views on the solar dynamo are being offered and targets for future research are highlighted.

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“…In order to do this, we use the test-field method, introduced in the geodynamo context by Schrinner et al (2005Schrinner et al ( , 2007 and currently available in the Pencil Code (e.g. Brandenburg 2005b;Brandenburg et al 2008).…”

Section: Turbulent Transport Coefficientsmentioning

confidence: 99%

Dynamo action and magnetic buoyancy in convection simulations with vertical shear

Gómez

Käpylä

2011

A&A

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Context. A hypothesis for sunspot formation is the buoyant emergence of magnetic flux tubes created by the strong radial shear at the tachocline. In this scenario, the magnetic field has to exceed a threshold value before it becomes buoyant and emerges through the whole convection zone. Aims. We follow the evolution of a random seed magnetic field with the aim of study under what conditions it is possible to excite the dynamo instability and whether the dynamo generated magnetic field becomes buoyantly unstable and emerges to the surface as expected in the flux-tube context. Methods. We perform numerical simulations of compressible turbulent convection that include a vertical shear layer. Like the solar tachocline, the shear is located at the interface between convective and stable layers. Results. We find that shear and convection are able to amplify the initial magnetic field and form large-scale elongated magnetic structures. The magnetic field strength depends on several parameters such as the shear amplitude, the thickness and location of the shear layer, and the magnetic Reynolds number (Rm). Models with deeper and thicker tachoclines allow longer storage and are more favorable for generating a mean magnetic field. Models with higher Rm grow faster but saturate at slightly lower levels. Whenever the toroidal magnetic field reaches amplitudes greater a threshold value which is close to the equipartition value, it becomes buoyant and rises into the convection zone where it expands and forms mushroom shape structures. Some events of emergence, i.e. those with the largest amplitudes of the initial field, are able to reach the very uppermost layers of the domain. These episodes are able to modify the convective pattern forming either broader convection cells or convective eddies elongated in the direction of the field. However, in none of these events the field preserves its initial structure. The back-reaction of the magnetic field on the fluid is also observed in lower values of the turbulent velocity and in perturbations of approximately three per cent on the shear profile. Conclusions. The results indicate that buoyancy is a common phenomena when the magnetic field is amplified through dynamo action in a narrow layer. It is, however, very hard for the field to rise up to the surface without losing its initial coherence.

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Mean‐field view on rotating magnetoconvection and a geodynamo model

Cited by 160 publications

References 5 publications

Turbulence and its parameterization in accretion discs

Turbulence and its parameterization in accretion discs

Advances in Theory and Simulations of Large-Scale Dynamos

Dynamo action and magnetic buoyancy in convection simulations with vertical shear

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