Nonlinear theory of a “shear-current” effect and mean-field magnetic dynamos

Rogachevskii, I.; Kleeorin, N.

doi:10.1103/physreve.70.046310

Cited by 125 publications

(197 citation statements)

References 32 publications

(76 reference statements)

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“…(17)- (19), the termsN f , N h , andN g are determined by the third moments appearing due to the nonlinear terms; the source terms I f i j , I h i j , and I g i j , which contain the large-scale spatial derivatives of the mean magnetic and velocity fields, are given by Eqs. (A3)-(A6) in Rogachevskii & Kleeorin (2004). These terms determine turbulent magnetic diffusion and effects of nonuniform mean velocity on the mean electromotive force.…”

Section: Equations For the Second Momentsmentioning

confidence: 99%

“…(17)- (19) we use an approach that is similar to that applied in Rogachevskii & Kleeorin (2004). We take into account that in Eq.…”

Section: Equations For the Second Momentsmentioning

confidence: 99%

“…To close the system, we express the set of the thirdorder termsN M ≡N M (III) through the lower moments M (II) . We use the spectral τ approximation, which postulates that the deviations of the third-moment terms,N M (III) (k), from the contributions to these terms afforded by the background turbulence,N M (III,0) (k), are expressed through similar deviations of the second moments: (Orszag 1970;Pouquet et al 1976;Kleeorin et al 1990;Rogachevskii & Kleeorin 2004), where τ(k) is the scaledependent relaxation time, which can be identified with the correlation time of the turbulent velocity field for large Reynolds numbers. The quantities with the superscript (0) correspond to the background turbulence (see below).…”

Section: The τ-Approachmentioning

confidence: 99%

“…By contrast, the τ approach (Orszag 1970;Pouquet et al 1976;Kleeorin et al 1990;Rogachevskii & Kleeorin 2004) is used to determine the dependence of mean-field coefficients on the rotation rate. This can also be done with DNS ).…”

Section: Introductionmentioning

confidence: 99%

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Competition of rotation and stratification in flux concentrations

Losada

Brandenburg

Kleeorin

et al. 2013

A&A

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Context. In a strongly stratified turbulent layer, a uniform horizontal magnetic field can become unstable and spontaneously form local flux concentrations due to a negative contribution of turbulence to the large-scale (mean-field) magnetic pressure. This mechanism, which is called negative effective magnetic pressure instability (NEMPI), is of interest in connection with dynamo scenarios in which most of the magnetic field resides in the bulk of the convection zone and not at the bottom, as is often assumed. Recent work using mean-field hydromagnetic equations has shown that NEMPI becomes suppressed at rather low rotation rates with Coriolis numbers as low as 0.1. Aims. Here we extend these earlier investigations by studying the effects of rotation both on the development of NEMPI and on the effective magnetic pressure. We also quantify the kinetic helicity resulting from direct numerical simulations (DNS) with Coriolis numbers and strengths of stratification comparable to values near the solar surface and compare it with earlier work at smaller scale separation ratios. Further, we estimate the expected observable signals of magnetic helicity at the solar surface. Methods. To calculate the rotational effect on the effective magnetic pressure we consider both DNS and analytical studies using the τ approach. To study the effects of rotation on the development of NEMPI we use both DNS and mean-field calculations of the three-dimensional hydromagnetic equations in a Cartesian domain. Results. We find that the growth rates of NEMPI from earlier mean-field calculations are well reproduced with DNS, provided the Coriolis number is below 0.06. In that case, kinetic and magnetic helicities are found to be weak and the rotational effect on the effective magnetic pressure is negligible as long as the production of flux concentrations is not inhibited by rotation. For faster rotation, dynamo action becomes possible. However, there is an intermediate range of rotation rates where dynamo action on its own is not yet possible, but the rotational suppression of NEMPI is being alleviated. Conclusions. Production of magnetic flux concentrations through the suppression of turbulent pressure appears to be possible only in the uppermost layers of the Sun, where the convective turnover time is less than two hours.

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Section: Equations For the Second Momentsmentioning

confidence: 99%

“…(17)- (19) we use an approach that is similar to that applied in Rogachevskii & Kleeorin (2004). We take into account that in Eq.…”

Section: Equations For the Second Momentsmentioning

confidence: 99%

Section: The τ-Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Competition of rotation and stratification in flux concentrations

Losada

Brandenburg

Kleeorin

et al. 2013

A&A

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“…Nevertheless, recent studies have shown that mean-field dynamo action is possible due to non-helical turbulence and shear (Brandenburg 2005a;Yousef et al 2008a,b;Brandenburg et al 2008). The nature of this dynamo is not yet entirely clear and may be attributed to the so called shear-current effect (Rogachevskii & Kleeorin 2003, 2004 or to the incoherent (stochastic) α-effect (Vishniac & Brandenburg 1997). According to Brandenburg et al (2008) the latter explanation is consistent with the turbulent transport coefficients.…”

Section: Introductionmentioning

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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