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Covas, Eurico; Tworkowski, Andrew; Tavakol, Reza; Brandenburg, Axel

doi:10.1023/a:1004923924011

Cited by 31 publications

(38 citation statements)

References 5 publications

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“…We have not observed any evidence of chaotic behaviour in the range of magnetic Reynolds number 20 ≤ R m ≤ 2 × 10 5 for supercritical α ≤ 4α c in agreement with Covas et al (1997). However, if the α effect is highly supercritical, the dynamical quenching formula for α M is insufficient for dynamo saturation, and additional algebraic quenching terms are needed (Kleeorin & Rogachevskii 1999).…”

Section: Secondary Dynamo Waves With Fsupporting

confidence: 75%

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: Secondary Dynamo Waves With Fsupporting

confidence: 75%

Magnetic helicity fluxes in interface and flux transport dynamos

Chatterjee

Gómez

Brandenburg

2010

A&A

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“…In Covas et al [2], the models were taken to be antisymmetric with respect to the equator and it was found that the minimum truncation order N for which a similar asymptotic behaviour existed was N = 4. Here in view of computational costs, we take this value of N for which the set of truncated equations becomes: 15) where D is the control parameter, the so called dynamo number, and ν = νt ηt which for compatibility with [2,10] we take to be ν = 0.5.…”

Section: The Modelmentioning

confidence: 99%

“…A coarse study of the system (2.10) -(2.15) and higher truncations was reported in [2] from a different point of view. Here we demonstrate the occurrence of crisis-induced intermittency in this system by considering the detailed nature of its attractors, their basins and especially their metamorphoses (merging), while treating D as the control parameter.…”

Section: Crisis-induced Intermittencymentioning

confidence: 99%

Crisis-induced intermittency in truncated mean field dynamos

Covas

Tavakol

1997

Phys. Rev. E

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We investigate the detailed dynamics of a truncated αω dynamo model with a dynamic α effect. We find the presence of multiple attractors, including two chaotic attractors with a fractal basin boundary which merge to form a single attractor as the control parameter is increased. By considering phase portraits and the scaling of averaged times of transitions between the two attractors, we demonstrate that this merging is accompanied by a crisis-induced intermittency. We also find a range of parameter values over which the system has a fractal parameter dependence for fixed initial conditions. This is the first time this type of intermittency has been observed in a dynamo model and it could be of potential importance in accounting for some forms of intermittency in the solar and stellar output.

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“…A quantitative model for the flux of magnetic helicity was proposed by Kleeorin & Rogachevskii (1999) and Kleeorin et al (2000). Note that Schmalz & Stix (1991), Covas et al (1998) and Blackman & Brandenburg (2002) have also investigated related solar dynamo models that included a dynamical equation describing the evolution of magnetic helicity. Magnetic helicity transport through the boundary of a dynamo region is reported by Chae (2001) to be observable at the solar surface.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear magnetic diffusion and magnetic helicity transport in galactic dynamos

Kleeorin¹,

Moss²,

Rogachevskii³

et al. 2003

A&A

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Abstract.We have extended our previous mean-field galactic dynamo model which included algebraic and dynamic alpha nonlinearities (Kleeorin et al. 2002), to include also a quenching of the turbulent diffusivity. We readily obtain equilibrium states for the large-scale magnetic field in the local disc dynamo model, and these fields have strengths that are comparable to the equipartition field strength. We find that the algebraic nonlinearity alone (i.e. quenching of both the α effect and turbulent magnetic diffusion) cannot saturate the growth of the mean magnetic field; only the combined effect of algebraic and dynamic nonlinearities can limit the growth of the mean magnetic field. However, in contrast to our earlier work without quenching of the turbulent diffusivity, we cannot now find satisfactory solutions in the no-z approximation to the axisymmetric galactic dynamo problem.

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Untitled

Cited by 31 publications

References 5 publications

Magnetic helicity fluxes in interface and flux transport dynamos

Magnetic helicity fluxes in interface and flux transport dynamos

Crisis-induced intermittency in truncated mean field dynamos

Nonlinear magnetic diffusion and magnetic helicity transport in galactic dynamos

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