Scale dependence of alpha effect and turbulent diffusivity

Brandenburg, Axel; Rädler, K.-H.; Schrinner, M.

doi:10.1051/0004-6361:200809365

Cited by 92 publications

(145 citation statements)

References 23 publications

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“…However, given that simulations now indicate that q s ≈ 0 (or perhaps even negative), this proposal would thus not be an option, unless some other as yet unexplored effect begins to play a role. In principle, all turbulent transport processes are nonlocal and must be described by a convolution with the mean field rather than a multiplication (Brandenburg et al 2008). In Fourier space, the convolution corresponds to a multiplication with a wavenumber-dependent turbulent transport coefficient.…”

Section: Discussionmentioning

confidence: 99%

Properties of the negative effective magnetic pressure instability

et al. 2012

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As was demonstrated in earlier studies, turbulence can result in a negative contribution to the effective mean magnetic pressure, which, in turn, can cause a large-scale instability. In this study, hydromagnetic mean-field modelling is performed for an isothermally stratified layer in the presence of a horizontal magnetic field. The negative effective magnetic pressure instability (NEMPI) is comprehensively investigated. It is shown that, if the effect of turbulence on the mean magnetic tension force vanishes, which is consistent with results from direct numerical simulations of forced turbulence, the fastest growing eigenmodes of NEMPI are two-dimensional. The growth rate is found to depend on a parameter β characterizing the turbulent contribution of the effective mean magnetic pressure for moderately strong mean magnetic fields. A fit formula is proposed that gives the growth rate as a function of turbulent kinematic viscosity, turbulent magnetic diffusivity, the density scale height, and the parameter β . The strength of the imposed magnetic field does not explicitly enter provided the location of the vertical boundaries are chosen such that the maximum of the eigenmode of NEMPI fits into the domain. The formation of sunspots and solar active regions is discussed as possible applications of NEMPI.

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Section: Discussionmentioning

confidence: 99%

Properties of the negative effective magnetic pressure instability

et al. 2012

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“…However the length scale of the magnetic field in Figs.10b, c and 11a, c, e is comparable to k −1 f , which suggests that the degree of scale separation may have become insufficient to write the electromotive force as a simple multiplication, as is done in the expression E = αB−η t J. Then it may become necessary to write the electromotive force as a convolution, which essentially corresponds to a low-pass filter (see, e.g., Brandenburg et al 2008). However, we have not pursued this aspect any further.…”

Section: Supercritical Diffusive Magnetic Helicity Fluxesmentioning

confidence: 98%

Magnetic helicity fluxes in interface and flux transport dynamos

Chatterjee

Gómez

Brandenburg

2010

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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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“…2) indicate that at least the pumping effect can experience not only a change in magnitude but also a qualitative change when the wavenumber of the test field is varied (for corresponding details see Brandenburg et al 2008b). It is of great interest to study whether similar effects can occur for the α-effect.…”

Section: Dependence On Wavenumber Kmentioning

confidence: 99%

Alpha effect and turbulent diffusion from convection

Käpylä¹,

Korpi²,

Brandenburg

2009

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Aims. We study turbulent transport coefficients that describe the evolution of large-scale magnetic fields in turbulent convection. Methods. We use the test field method, together with three-dimensional numerical simulations of turbulent convection with shear and rotation, to compute turbulent transport coefficients describing the evolution of large-scale magnetic fields in mean-field theory in the kinematic regime. We employ one-dimensional mean-field models with the derived turbulent transport coefficients to examine whether they give results that are compatible with direct simulations. Results. The results for the α-effect as a function of rotation rate are consistent with earlier numerical studies, i.e. increasing magnitude as rotation increases and approximately cos θ latitude profile for moderate rotation. Turbulent diffusivity, η t , is proportional to the square of the turbulent vertical velocity in all cases. Whereas η t decreases approximately inversely proportional to the wavenumber of the field, the α-effect and turbulent pumping show a more complex behaviour with partial or full sign changes and the magnitude staying roughly constant. In the presence of shear and no rotation, a weak α-effect is induced which does not seem to show any consistent trend as a function of shear rate. Provided that the shear is large enough, this small α-effect is able to excite a dynamo in the mean-field model. The coefficient responsible for driving the shear-current effect shows several sign changes as a function of depth but is also able to contribute to dynamo action in the mean-field model. The growth rates in these cases are, however, well below those in direct simulations, suggesting that an incoherent α-shear dynamo may also act in the simulations. If both rotation and shear are present, the α-effect is more pronounced. At the same time, the combination of the shear-current and Ω × J-effects is also stronger than in the case of shear alone, but subdominant to the α-shear dynamo. The results of direct simulations are consistent with mean-field models where all of these effects are taken into account without the need to invoke incoherent effects.

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Scale dependence of alpha effect and turbulent diffusivity

Cited by 92 publications

References 23 publications

Properties of the negative effective magnetic pressure instability

Properties of the negative effective magnetic pressure instability

Magnetic helicity fluxes in interface and flux transport dynamos

Alpha effect and turbulent diffusion from convection

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