The α-effect in 2D fast dynamos

Courvoisier, Alice

doi:10.1080/03091920701562095

Cited by 10 publications

(12 citation statements)

References 25 publications

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“…The symmetry properties of the MW+ flow imply that there is no AKA effect and that its kinematic α tensor is diagonal, with entries α 11 = α 22 = α; these have been computed numerically by Courvoisier (2008). We use this example to illustrate the fact that taking only magnetic perturbations into account can be misleading.…”

Section: Numerical Example Ii: Modulated Wave (Mw+) Forcing (A) the Bmentioning

confidence: 99%

Self-consistent mean-field magnetohydrodynamics

2009

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We consider the linear stability of two-dimensional nonlinear magnetohydrodynamic basic states to long-wavelength three-dimensional perturbations. Following Hughes & Proctor (Hughes & Proctor 2009 Proc. R. Soc. A 465, 1599-1616 (doi:10.1098/rspa.2008.0493)), the two-dimensional basic states are obtained from a specific forcing function in the presence of an initially uniform mean field of strength B. By extending to the nonlinear regime the kinematic analysis of Roberts (Roberts 1970 Phil. Trans. R. Soc. Lond. A 266, 535-558 (doi:10.1098/rsta.1970.0011)), we show that it is possible to predict the growth rate of these perturbations by applying mean-field theory to both the momentum and the induction equations. If B = 0, these equations decouple and large-scale magnetic and velocity perturbations may grow via the kinematic α-effect and the anisotropic kinetic alpha instability, respectively. However, if B = 0, the momentum and induction equations are coupled by the Lorentz force; in this case, we show that four transport tensors are now necessary to determine the growth rate of the perturbations. We illustrate these situations by numerical examples; in particular, we show that a mean-field description of the nonlinear regime based solely on a quenched α coefficient is incorrect.

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Section: Numerical Example Ii: Modulated Wave (Mw+) Forcing (A) the Bmentioning

confidence: 99%

Self-consistent mean-field magnetohydrodynamics

2009

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“…The main motivation for the present paper were the results reported by Courvoisier, Hughes & Tobias (2006, hereafter CHT06) and Courvoisier (2008) on α and γ effects in GP flows. They found that there is a complicated dependence of α on the magnetic Reynolds number R m and on parameters defining the flow, with sign changes and no indication of convergence with increasing R m , and ‘no clear relation between α and the helicity of the flow, contrary to what is often assumed for the parametrization of mean‐field dynamo models’.…”

Section: Introductionmentioning

confidence: 99%

Mean-field effects in the Galloway-Proctor flow

Rädler

Brandenburg

2009

Monthly Notices of the Royal Astronomical Society

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The coefficients defining the mean electromotive force in a Galloway-Proctor flow are determined. This flow shows a two-dimensional pattern and is helical. The pattern wobbles in its plane. Apart from one exception a circular motion of the flow pattern is assumed. This corresponds to one of the cases considered recently by Courvoisier, Hughes and Tobias (2006, Phys. Rev. Lett., 96, 034503). An analytic theory of the alpha effect and related effects in this flow is developed within the second-order correlation approximation and a corresponding fourth-order approximation. In the validity range of these approximations there is an alpha effect but no gamma effect, or pumping effect. Numerical results obtained with the test-field method, which are independent of these approximations, confirm the results for alpha and show that gamma is in general nonzero. Both alpha and gamma show a complex dependency on the magnetic Reynolds number and other parameters that define the flow, that is, amplitude and frequency of the wobbling motion. Some results for the magnetic diffusivity eta_t and a related quantity are given, too. Finally a result for alpha in the case of a randomly varying flow without the aforementioned circular motion is presented. This flow may be a more appropriate model for studying the alpha effect and related effects in flows that are statistical isotropic in a plane.Comment: 12 pages, 14 figures, submitted to MNRA

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“…steady or time-periodic) flows by incorporating separately, and in a controlled manner, temporal and spatial decoherence. The former problem has been studied by Courvoisier et al (2006) and Courvoisier (2008), who demonstrated that increasing temporal decoherence leads to a reduction in the magnitude and Rm-dependence of the α-effect. Here we address the complementary question of the influence on the transport coefficients of spatial decorrelation.…”

Section: Introductionmentioning

confidence: 99%

Mean induction and diffusion: the influence of spatial coherence

2009

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Within the same framework we calculate the mean induction of a magnetic field and the mean diffusivity of a passive scalar, for two families of flows in which the degree of spatial decorrelation can be systematically adjusted. We investigate the dependence of these quantities both on the spatial decoherence and on the molecular diffusivity. We demonstrate that for flows with similar global properties, the mean induction is dramatically reduced as the flows become less spatially correlated; the mean diffusivity, on the other hand, shows no significant or systematic variation.

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The α-effect in 2D fast dynamos

Cited by 10 publications

References 25 publications

Self-consistent mean-field magnetohydrodynamics

Self-consistent mean-field magnetohydrodynamics

Mean-field effects in the Galloway-Proctor flow

Mean induction and diffusion: the influence of spatial coherence

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