Finite amplitude convection and magnetic field generation in a rotating spherical shell

Zhang, Ke-Ke; Busse, F. H.

doi:10.1080/03091928808208877

Cited by 109 publications

(30 citation statements)

References 7 publications

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“…The work by Glatzmaier and Roberts (1995a) marked a first highlight after previous authors had proven the general validity of the concept (Zhang and Busse 1988). Since then, several new numerical codes have been developed that mostly aim at modeling the geodynamo.…”

Section: Introductionmentioning

confidence: 99%

Theory and Modeling of Planetary Dynamos

Wicht

Tilgner

2010

Space Sci Rev

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Numerical dynamo models are increasingly successful in modeling many features of the geomagnetic field. Moreover, they have proven to be a useful tool for understanding how the observations connect to the dynamo mechanism. More recently, dynamo simulations have also ventured to explain the surprising diversity of planetary fields found in our solar system. Here, we describe the underlying model equations, concentrating on the Boussinesq approximations, briefly discuss the numerical methods, and give an overview of existing model variations. We explain how the solutions depend on the model parameters and introduce the primary dynamo regimes. Of particular interest is the dependence on the Ekman number which is many orders of magnitude too large in the models for numerical reasons. We show that a minor change in the solution seems to happen at E = 3×10 −6 whose significance, however, needs to be explored in the future. We also review three topics that have been a focus of recent research: field reversal mechanisms, torsional oscillations, and the influence of Earth's thermal mantle structure on the dynamo. Finally we discuss the possibility of tidally or precession driven planetary dynamos.

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Section: Introductionmentioning

confidence: 99%

Theory and Modeling of Planetary Dynamos

Wicht

Tilgner

2010

Space Sci Rev

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“…Since the first full numerical models of dynamo action (Zhang & Busse 1988, Zhang & Busse 1989, Glatzmaier & Roberts 1995, many parameter space surveys have been performed. This has allowed to produce phase-diagrams which, depending on the controlling parameters, describe which dynamo states can be achieved.…”

Section: Introductionmentioning

confidence: 99%

Three branches of dynamo action

2018

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Abstract.In addition to the weak-dipolar state and to the fluctuating-multipolar state, widely discussed in the literature, a third regime has been identified in (Dormy 2016). It corresponds to a strong-dipolar branch which appears to approach, in a numerically affordable regime, the magnetostrophic limit relevant to the dynamics of the Earth's core. We discuss the transitions between these states and point to the relevance to this strong-dipolar state to Geodynamo modelling.

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“…Some progress has been made in this direction (e.g. Soward, 1986;Soward and Skinner, 1988;Fearn and Proctor, 1987;Zhang and Busse;1988), but the full program has not yet been carried out. A simpler, but in some ways less satisfactory, approach is to make use of mean-field electrodynamics to separate the dynamo problem into two parts: the motions generating the helicity are assumed to take place on small length scales, which are further assumed to be dynamically decoupled from the large scale motions.…”

Section: Introductionmentioning

confidence: 97%

αω-Dynamos and Taylor's constraint

Abdel-Aziz¹,

Jones²

1988

Geophysical & Astrophysical Fluid Dynamics

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Plane layer aw-dynamo models are investigated. Travelling wave solutions are found: two critical dynamo numbers are shown to exist. At the first, D,, dynamo action becomes possible. As D is increased above D,, a regime is entered where core-mantle coupling is an essential part of the problem. At a second critical dynamo number, D,, Taylor's constraint is satisfied. As D is raised beyond this value, nonlinear inviscid ageostrophic solutions satisfying Taylor's constraint have been computed.

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Finite amplitude convection and magnetic field generation in a rotating spherical shell

Cited by 109 publications

References 7 publications

Theory and Modeling of Planetary Dynamos

Theory and Modeling of Planetary Dynamos

Three branches of dynamo action

αω-Dynamos and Taylor's constraint

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