Magnetic Diffusivity Tensor and Dynamo Effects in Rotating and Shearing Turbulence

Brandenburg, Axel; Rädler, K.-H.; Rheinhardt, M.; Käpylä, Petri J.

doi:10.1086/527373

Cited by 145 publications

(338 citation statements)

References 38 publications

(58 reference statements)

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“…However, our definition of the Reynolds number depends on k f (=2π/d) which is not as well defined as in, e.g., forced turbulence simulations, so the coefficients may depend on η for values somewhat larger than Rm = 1 in the present case. These results agree with those obtained for isotropic turbulence (Sur et al 2008;Brandenburg et al 2008a;Mitra et al 2009). …”

Section: Dependence On Rmsupporting

confidence: 91%

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Alpha effect and turbulent diffusion from convection

Käpylä¹,

Korpi²,

Brandenburg

2009

A&A

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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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Section: Dependence On Rmsupporting

confidence: 91%

“…Similar results, i.e. monotonically decreasing η t and a first increasing and then decreasing δ were obtained from forced turbulence simulations by Brandenburg et al (2008a).…”

Section: Dependence On Cosupporting

confidence: 86%

Alpha effect and turbulent diffusion from convection

Käpylä¹,

Korpi²,

Brandenburg

2009

A&A

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“…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: Introductionsupporting

confidence: 64%

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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“…One may wonder how generic such fluctuations are and if such fluctuations could be relevant for say the incoherent dynamo effects that have been investigated by several authors in recent years (Vishniac & Brandenburg 1997;Sur & Subramanian 2009;Heinemann et al 2011;Mitra & Brandenburg 2012;Richardson & Proctor 2010). It will therefore be interesting the associate the kinetic helicity fluctuations with those of α, which have already been determined in simulations of turbulent shear flows (Brandenburg et al 2008).…”

Section: Discussionmentioning

confidence: 97%

Kinetic helicity decay in linearly forced turbulence

Brandenburg

Petrosyan

2012

Astron Nachr

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The decay of kinetic helicity is studied in numerical models of forced turbulence using either an externally imposed forcing function as an inhomogeneous term in the equations or, alternatively, a term linear in the velocity giving rise to a linear instability. The externally imposed forcing function injects energy at the largest scales, giving rise to a turbulent inertial range with nearly constant energy flux while for linearly forced turbulence the spectral energy is maximum near the dissipation wavenumber. Kinetic helicity is injected once a statistically steady state is reached, but it is found to decay on a turbulent time scale regardless of the nature of the forcing and the value of the Reynolds number.

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Magnetic Diffusivity Tensor and Dynamo Effects in Rotating and Shearing Turbulence

Cited by 145 publications

References 38 publications

Alpha effect and turbulent diffusion from convection

Alpha effect and turbulent diffusion from convection

Dynamo action and magnetic buoyancy in convection simulations with vertical shear

Kinetic helicity decay in linearly forced turbulence

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