Kinematic α-effect in isotropic turbulence simulations

Sur, Sharanya; Brandenburg, Axel; Subramanian, Kandaswamy

doi:10.1111/j.1745-3933.2008.00423.x

Cited by 97 publications

(131 citation statements)

References 24 publications

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“…The turbulent coefficients α and η t in these equations are estimated as follows: from the mixing length theory we know that the turbulent diffusivity in the convection zone is given by (cf. Sur et al 2008) …”

Section: Interface Dynamomentioning

confidence: 99%

Magnetic helicity fluxes in interface and flux transport dynamos

Chatterjee

Gómez

Brandenburg

2010

A&A

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Context. Dynamos in the Sun and other bodies tend to produce magnetic fields that possess magnetic helicity of opposite sign at large and small scales, respectively. The build-up of magnetic helicity at small scales provides an important saturation mechanism. Aims. In order to understand the nature of the solar dynamo we need to understand the details of the saturation mechanism in spherical geometry. In particular, we aim to understand the effects of magnetic helicity fluxes from turbulence and meridional circulation. Methods. We consider a model with only radial shear confined to a thin layer (tachocline) at the bottom of the convection zone. The kinetic α owing to helical turbulence is assumed to be localized in a region above the convection zone. The dynamical quenching formalism is used to describe the build-up of mean magnetic helicity in the model, which results in a magnetic α effect that feeds back on the kinetic α effect. In some cases we compare these results with those obtained from a model with a simple algebraic α quenching formula.Results. In agreement with earlier findings, the magnetic α effect has the opposite sign compared with the kinetic α effect and leads to a catastrophic decrease of the saturation field strength proportional to the inverse magnetic Reynolds number. At high latitudes this quenching effect can lead to secondary dynamo waves that propagate poleward because of the opposite sign of α. These secondary dynamo waves are driven by small-scale magnetic helicity instead of the small-scale kinetic helicity. Magnetic helicity fluxes both from turbulent mixing and from meridional circulation alleviate catastrophic quenching. Interestingly, supercritical diffusive helicity fluxes also give rise to secondary dynamo waves and grand minima-like episodes.

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Section: Interface Dynamomentioning

confidence: 99%

Magnetic helicity fluxes in interface and flux transport dynamos

Chatterjee

Gómez

Brandenburg

2010

A&A

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“…Let us return once more to the coefficients α and β for homogeneous isotropic turbulence. Referring to numerical simulations of hydrodynamic turbulence in a weakly compressible fluid, Sur et al (2008) used the test-field method for the determination of these coefficients. The turbulence was specified to have an energy input at a wavenumber k f , and to be maximally helical, that is, (∇ × u) 2 /u 2 = k 2 f .…”

Section: Test-field Methodsmentioning

confidence: 99%

Mean‐field dynamos: The old concept and some recent developments

Rädler

2014

Astron Nachr

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This article elucidates the basic ideas of electrodynamics and magnetohydrodynamics of mean fields in turbulently moving conducting fluids. It is stressed that the connection of the mean electromotive force with the mean magnetic field and its first spatial derivatives is in general neither local nor instantaneous and that quite a few claims concerning pretended failures of the mean-field concept result from ignoring this aspect. In addition to the mean-field dynamo mechanisms of α 2 and αΩ type several others are considered. Much progress in mean-field electrodynamics and magnetohydrodynamics results from the test-field method for calculating the coefficients that determine the connection of the mean electromotive force with the mean magnetic field. As an important example the memory effect in homogeneous isotropic turbulence is explained. In magnetohydrodynamic turbulence there is the possibility of a mean electromotive force that is primarily independent of the mean magnetic field and labeled as Yoshizawa effect. Despite of many efforts there is so far no convincing comprehensive theory of α quenching, that is, the reduction of the α effect with growing mean magnetic field, and of the saturation of mean-field dynamos. Steps toward such a theory are explained. Finally, some remarks on laboratory experiments with dynamos are made.

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“…Using the estimate η t = u rms /3k f (Sur et al 2008), our choice of η t implies that the normalized wavenumber of the energy-carrying eddies is k f R =ũ rms /3η t ≈ 120 and that k f H p0 varies between 6.2 (for r /R = 1.1) and 2.3 (for r /R = 1.001).…”

Section: The Modelmentioning

confidence: 99%

Surface flux concentrations in a sphericalα²dynamo

Jabbari

Brandenburg

Kleeorin

et al. 2013

A&A

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Context. In the presence of strong density stratification, turbulence can lead to the large-scale instability of a horizontal magnetic field if its strength is in a suitable range (around a few percent of the turbulent equipartition value). This instability is related to a suppression of the turbulent pressure so that the turbulent contribution to the mean magnetic pressure becomes negative. This results in the excitation of a negative effective magnetic pressure instability (NEMPI). This instability has so far only been studied for an imposed magnetic field. Aims. We want to know how NEMPI works when the mean magnetic field is generated self-consistently by an α 2 dynamo, whether it is affected by global spherical geometry, and whether it can influence the properties of the dynamo itself. Methods. We adopt the mean-field approach, which has previously been shown to provide a realistic description of NEMPI in direct numerical simulations. We assume axisymmetry and solve the mean-field equations with the Pencil Code for an adiabatic stratification at a total density contrast in the radial direction of ≈4 orders of magnitude. Results. NEMPI is found to work when the dynamo-generated field is about 4% of the equipartition value, which is achieved through strong α quenching. This instability is excited in the top 5% of the outer radius, provided the density contrast across this top layer is at least 10. NEMPI is found to occur at lower latitudes when the mean magnetic field is stronger. For weaker fields, NEMPI can make the dynamo oscillatory with poleward migration. Conclusions. NEMPI is a viable mechanism for producing magnetic flux concentrations in a strongly stratified spherical shell in which a magnetic field is generated by a strongly quenched α effect dynamo.

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Kinematic α-effect in isotropic turbulence simulations

Cited by 97 publications

References 24 publications

Magnetic helicity fluxes in interface and flux transport dynamos

Magnetic helicity fluxes in interface and flux transport dynamos

Mean‐field dynamos: The old concept and some recent developments

Surface flux concentrations in a sphericalα²dynamo

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Kinematic α-effect in isotropic turbulence simulations

Cited by 97 publications

References 24 publications

Magnetic helicity fluxes in interface and flux transport dynamos

Magnetic helicity fluxes in interface and flux transport dynamos

Mean‐field dynamos: The old concept and some recent developments

Surface flux concentrations in a sphericalα2dynamo

Contact Info

Product

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Surface flux concentrations in a sphericalα²dynamo