On the α‐effect for slow and fast rotation

Rüdiger, G.

doi:10.1002/asna.19782990408

Cited by 59 publications

(42 citation statements)

References 11 publications

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“…The α-effect is a nontrivial tensor if the rotation is fast: 1970;Rüdiger 1978;Busse & Miin 1979) where α zz refers to the α-effect in cylindrical coordinates and z denotes the direction parallel to the rotation axis. The tensorial structure of the α-effect is now taken into account, i.e.…”

Section: Non-axisymmetric Modesmentioning

confidence: 99%

Oscillatingα 2-dynamos and the reversal phenomenon of the global geodynamo

2005

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Abstract. A geodynamo-model based on an α-effect which has been computed under conditions suitable for the geodynamo is constructed. For a highly restricted class of radial α-profiles the linear α 2 -model exhibits oscillating solutions on a timescale given by the turbulent diffusion time. The basic properties of the periodic solutions are presented and the influence of the inner core size on the characteristics of the critical range that allows for oscillating solutions is shown. Reversals are interpreted as half of such an oscillation. They are rather seldom events because they can only occur if the α-profile exists long enough within the small critical range that allows for periodic solutions. Due to strong fluctuations on the convective timescale the probability of such a reversal is very small. Finally, a simple non-linear mean-field model with reasonable input parameters based on simulations of Giesecke et al. (2005) demonstrates the plausibility of the presented theory with a long-time series of a (geo-)dynamo reversal sequence.

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Section: Non-axisymmetric Modesmentioning

confidence: 99%

Oscillatingα 2-dynamos and the reversal phenomenon of the global geodynamo

2005

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“…As an application of this work, comparisons between the spectral equations and analysis developed here and that of Ru¨diger (1978Ru¨diger ( , 1980, Busse and Miin (1979) and Kono and Roberts (1994) reveal differences. Moreover, Phillips (1993) was used by Kono and Roberts (1994) to compare numerical results and conclude that the results of Kono and Roberts (1994) were correct, and hence those of Phillips (1993) were incorrect.…”

Section: Discussionmentioning

confidence: 83%

“…Ru¨diger (1978) re-established the result of Moffatt (1970) for fast rotation with A ¼ 1 in the a tensor a ¼ cos ðI À AẑẑÞ with ¼ constant:…”

Section: Previous Investigations Of Anisotropic Alpha-effects Under Tmentioning

confidence: 82%

Vector and scalar spherical harmonic spectral equations for rapidly rotating anisotropic alpha-effect dynamos

Phillips

2013

Geophysical & Astrophysical Fluid Dynamics

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Spectral equations are derived for a mean field induction equation, qB=qt À r 2 B ¼ R; Â F with an a-effect, considered appropriate for rapid rotation, given bywhere ðx,ŷ,ẑÞ are Cartesian unit vectors, a 1 (r, , ), a 3 (r, , ) are scalar functions of position, (r, , ) are spherical polar coordinates and R is the magnetic Reynolds number. The effect of rotation on convection for different boundaries and parameters is discussed. The effect of the flow structure on a for different geostrophic and near geostrophic models is analysed. The vector spherical harmonicswhere e À1 ¼ ðx À iŷÞ=2 1=2 , e 0 ¼ẑ, e 1 ¼ Àðx þ iŷÞ=2 1=2 , the 2 Â 3 matrix is a Wigner 3J coefficient and Y m n ¼ Y m n ð, Þ are scalar spherical harmonics, are used to derive the vector Y m n,n1 forms of the induction equation for this a-effect. The solenoidal condition ; · B ¼ 0 is imposed by relating the Y m n,n1 formalism to the toroidal-poloidal harmonic formalism, T m n ¼ ; Â ðrT m n Y m n Þ and S m n ¼ ; Â ; Â ðrS m n Y m n Þ. The T m n and S m n components of the induction equation are thus derived in terms of F m n,n1 , the Y m n,n1 components of F; F ¼ P nþ1 n1¼nÀ1 P n m¼Àn P 1 n¼0 F m n,n1 Y m n,n1 . These combined T m n /Y m n,n1 , S m n /Y m n,n1 vector spectral equations are then transformed into interaction type ða na S equations for the isotropic and anisotropic components of a. As an application of the general spectral equations derived herein, the interaction equations can be specialised by restricting a 1 and a 3 to be proportional to r cos or cos , or restricting B and a to be axisymmetric. These equations are then compared to those of previous works. The differences between the equations derived herein and those of past works provide corrections and account for, at least in part, the differences in numerical solutions of the past works.

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“…Rüdiger 1978, Rädler 1980. Weisshaar (1982) presented an a 2 -dynamo model with a solarlike behaviour (butterfly diagram, period) with anisotropies a r r < 0, ags -α φ ψ > Ο,α Γ 0 = Οίθν > 0 and |α ΓΓ | > At that time the author considered his extensor as rather unrealistic.…”

Section: Magnetic Field Structure and Dynamo Theory In The Convectionmentioning

confidence: 99%

The Solar Dynamo

Schmitt

1993

Symp. - Int. Astron. Union

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A b s t r a c t . The generation of the solar magnetic field is generally ascribed to dynamo processes in the convection zone. The dynamo effects, differential rotation (u;-effect) and helical turbulence ( aeffect) are explained, and the basic properties of the mean-field dynamo equations are discussed in close comparison with the observed solar cycle.Especially the question of the seat of the dynamo is addressed. Problems of a dynamo in the convection zone proper could be magnetic buoyancy, the nearly strict observance of the polarity rules and the migration pattern of the magnetic fields which are difficult to understand in the light of recent studies of the field structure in the convection zone and by observations of the solar acoustic oscillations. To overcome some of these problems it has been suggested that the solar dynamo operates in the thin overshoot region at the base of the convection zone instead. Some aspects of such an interface dynamo are discussed. As an alternative to the turbulent α-effect a dynamic α-effect based on magnet ostrophic waves driven by a magnetic buoyancy instability of a magnetic flux layer is introduced. Model calculations for both pictures, a convection zone and an interface dynamo, are presented which use the internal rotation of the sun as deduced from helioseismology. Solutions with solar cycle behaviour are only obtained if the magnetic flux is bounded in the lower convection zone and the α-effect is concentrated near the equator.Another aspect briefly addressed is the nonlinear saturation of the magnetic field. The necessity of the dynamic nature of the dynamo processes is emphasized, and different processes, e.g. magnetic buoyancy and α-quenching, are mentioned. K e y words: Mean-Field Electrodynamics -Dynamo Theory -Sun

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On the α‐effect for slow and fast rotation

Cited by 59 publications

References 11 publications

Oscillatingα 2-dynamos and the reversal phenomenon of the global geodynamo

Oscillatingα 2-dynamos and the reversal phenomenon of the global geodynamo

Vector and scalar spherical harmonic spectral equations for rapidly rotating anisotropic alpha-effect dynamos

The Solar Dynamo

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