Numerical simulations of stellar convective dynamos. I. the model and method

Glatzmaier, Gary A.

doi:10.1016/0021-9991(84)90033-0

Cited by 422 publications

(360 citation statements)

References 45 publications

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“…Chebychev polynomials C n (r) are typically chosen for the spectral representation in radius. When applied appropriately, they provide a denser radial grid near the inner and outer boundaries where boundary layers may have to be sampled (Glatzmaier 1984;Christensen and Wicht 2007).…”

Section: Methodsmentioning

confidence: 99%

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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: Methodsmentioning

confidence: 99%

“…A recent overview of local methods can be found in Wicht et al (2009). More information on the pseudo-spectral method can be found in Glatzmaier (1984) and Christensen and Wicht (2007). The dynamo benchmarks defined by Christensen et al (2001) serve as test cases for the various methods; an update can be found in Wicht et al (2009).…”

Section: Methodsmentioning

confidence: 99%

Theory and Modeling of Planetary Dynamos

Wicht

Tilgner

2010

Space Sci Rev

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“…Although the equations do not decouple in the linear part, and we must treat meanflows separately, the formulation is similar to that used by Glatzmaier (1984) in spherical geometry. We use potentials for the velocity yet do not eliminate the pressure.…”

Section: Discussionmentioning

confidence: 99%

“…As the pressure has not been eliminated, we also take the divergence of the momentum equation. A single-curl formulation was proposed by Glatzmaier (1984) in the spherical geometry and has proved very successful.…”

Section: Formulation and Solutionmentioning

confidence: 99%

Hydromagnetic Taylor–Couette flow: numerical formulation and comparison with experiment

Willis

Barenghi

2002

J. Fluid Mech.

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Taylor-Couette flow in the presence of a magnetic field is a problem belonging to classical hydromagnetics and deserves to be more widely studied than it has been to date. In the nonlinear regime the literature is scarce. We develop a formulation suitable for solution of the full three dimensional nonlinear hydromagnetic equations in cylindrical geometry, which is motived by the formulation for the magnetic field. It is suitable for study at finite Prandtl numbers and in the small Prandtl number limit, relevant to laboratory liquid metals. The method is used to determine the onset of axisymmetric Taylor vortices, and finite amplitude solutions. Our results compare well with existing linear and nonlinear hydrodynamic calculations and with hydromagnetic experiments.

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“…Since cx<0 in the boundary layer (Yoshimura 1975, Gilman 1983, Glatzmaier 1984, 1985a,b, Gilman et al 1989, Parker 1989, and, interpolating the hehoseismological results in the boundary layer:…”

Section: The Location Andwcrhng Mechanism Cf Dyn^rointhelohtcfheldsementioning

confidence: 95%

Solar and Stellar Cycles

Belvedère

1990

International Astronomical Union Colloquium

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ABSTRACT. The increasing observational evidence offered by photometric and spectroscopic data of magnetic cycles in lower main sequence stars, has confirmed the general expectation that the same basic dynamo mechanism operates in the Sun and main sequence in stars widi outer convective envelopes.Unfortunately, no clear correlation has been found, up to date, with stellar parameters as mass, rotation rate and age, even if irregular activity and shorter cycle periods seem to be characteristic of stars more massive than the Sun, while hyperactive fast rotating components of binary systems like RS CVn's and BY Dra's show a tendency for cycles as long as several decades.Although dynamo theory has probably captured die essential physics of the convection-rotation interaction giving rise to stellar magnetic activity, as evidenced, for instance, by the correlation between proxy activity, indicators and the Rossby parameter related to the dynamo number, the reliability of the present theoretical background should be measured by its capacity of interpreting and predicting characteristics and periodicities (or aperiodicities) of stellar cycles. This should be done in the framework of the nonlinear approach, which, in principle can describe multimodal dynamo behaviour with a variety of time scales.The fundamentals of the theory must be tested, however, in the closest astrophysical laboratory, our Sun. Serious problems to a dynamo mechanism operating in the convection zone have been posed by most recent helioseismological results, which, on the other hand, do not rule out the possibility of dynamo action in the transition layer between the convective and die radiative zones, which is suggested independently by the global solar cycle features. Indeed, assuming the correct sign of helicity in the transition layer, the helioseismological data on the radial gradient of angular velocity support both equatorward propagation of dynamo waves at lower latitudes and poleward propagation at higher latitudes, which is evidenced by different tracers of the solar cycle.

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Numerical simulations of stellar convective dynamos. I. the model and method

Cited by 422 publications

References 45 publications

Theory and Modeling of Planetary Dynamos

Theory and Modeling of Planetary Dynamos

Hydromagnetic Taylor–Couette flow: numerical formulation and comparison with experiment

Solar and Stellar Cycles

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