Equations governing convection in earth's core and the geodynamo

Braginsky, S. I.; Roberts, Paul

doi:10.1080/03091929508228992

Cited by 479 publications

(489 citation statements)

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“…Developing the general set of equation for the dynamo problem is beyond the scope of this paper; we refer to Braginsky and Roberts (1995). Here, we restrict ourselves to the simplified system provided by the Boussinesq approximation where the dissipation number,…”

Section: Basic Equationsmentioning

confidence: 99%

“…This approach is justified since the disturbances are indeed very small. The convective temperature disturbances, for example, amount to only 10 −6 times the adiabatic temperature drop across Earth's outer core (Braginsky and Roberts 1995;Jones 2007).…”

Section: Basic Equationsmentioning

confidence: 99%

“…Several publications provide extensive overviews of the different aspects in numerical dynamo simulations (Braginsky and Roberts 1995;Jones 2000Jones , 2007Glatzmaier 2002) and discuss their success in modeling the geomagnetic field (Kono and Roberts 2002;Christensen and Wicht 2007). Here, we concentrate on more recent developments that mainly concern the geodynamo.…”

Section: Introductionmentioning

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: Basic Equationsmentioning

confidence: 99%

Section: Basic Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Theory and Modeling of Planetary Dynamos

Wicht

Tilgner

2010

Space Sci Rev

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“…As a result, Ekman and magnetic Prandtl numbers are significantly larger in the models than would be appropriate. A simple way to parameterize small-scale turbulent mixing is to assume larger effective diffusivities that are of comparable magnitude for all diffusive effects (Braginsky and Roberts 1995). This argument is commonly cited to justify the combination of thermal and compositional effects into one codensity variable and motivates the choice of Pr = 1 in numerical dynamo simulations.…”

Section: Numerical Dynamo Modelsmentioning

confidence: 99%

“…4). In principle, T and χ obey two individual transport equations, which can be combined under the assumption that the effective (turbulent) thermal diffusivity κ T and compositional diffusivity κ χ are identical (Braginsky and Roberts 1995;Kutzner and Christensen 2004):…”

Section: Numerical Dynamo Modelsmentioning

confidence: 99%

The Origin of Mercury’s Internal Magnetic Field

Mandéa

Takahashi

Christensen

et al. 2008

Mercury

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Mariner 10 measurements proved the existence of a large-scale internal magnetic field on Mercury. The observed field amplitude, however, is too weak to be compatible with typical convective planetary dynamos. The Lorentz force based on an extrapolation of Mariner 10 data to the dynamo region is 10 −4 times smaller than the Coriolis force. This is at odds with the idea that planetary dynamos are thought to work in the so-called magnetostrophic regime, where Coriolis force and Lorentz force should be of comparable magnitude. Recent convective dynamo simulations reviewed here seem to resolve this caveat. We show that the available convective power indeed suffices to drive a magnetostrophic dynamo even when the heat flow though Mercury's core-mantle boundary is subadiabatic, as suggested by thermal evolution models. Two possible causes are analyzed that could explain why the observations do not reflect a stronger internal field. First, toroidal magnetic fields can be strong but are confined to the conductive core, and second, the observations do not resolve potentially strong small-scale contributions. We review different dynamo simulations that promote either or both effects by (1) strongly driving convection, (2) assuming a particularly small inner core, or (3) assuming a very large inner core. These models still fall somewhat short of explaining the low amplitude of Mariner 10 observations, but the incorporation of an additional effect helps to reach this goal: The subadiabatic heat flow through Mercury's core-mantle boundary may cause the outer part of the core to be stably stratified, which would largely exclude convective motions in this region. The magnetic field, which is small scale, strong, and very time dependent in the lower convective part of the core, must diffuse through the stagnant layer. Here, the electromagnetic skin effect filters out the more rapidly varying high-order contributions and mainly leaves behind the weaker and slower varying dipole and quadrupole components (Christensen in Nature 444: [1056][1057][1058] 2006). Messenger and BepiColombo data will allow us to discriminate between the various models in terms of the magnetic fields spatial structure, its degree of axisymmetry, and its secular variation.

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A dynamo explanation for Mercury's anomalous magnetic field

Cao

Aurnou

Wicht

et al. 2014

Geophysical Research Letters

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Recent MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) measurements have shown that Mercury's magnetic field is axial‐dominant, yet strongly asymmetric with respect to the equator: the field strength in the Northern Hemisphere is approximately 3 times stronger than that in the Southern Hemisphere. Here we show that convective dynamo models driven by volumetric buoyancy with north‐south symmetric thermal boundaries are capable of generating quasi‐steady north‐south asymmetric magnetic fields similar to Mercury's. This symmetry breaking is promoted and stabilized when the core‐mantle boundary heat flux is higher at the equator than at high latitudes. The equatorially asymmetric magnetic field generation in our dynamo models corresponds to equatorially asymmetric kinetic helicity, which results from mutual excitation of two different modes of columnar convection. Our dynamo model can be tested by future assessment of Mercury's magnetic field from MESSENGER and BepiColombo as well as through investigations on Mercury's lower mantle temperature heterogeneity and buoyancy forcing in Mercury's core.

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Equations governing convection in earth's core and the geodynamo

Cited by 479 publications

References 47 publications

Theory and Modeling of Planetary Dynamos

Theory and Modeling of Planetary Dynamos

The Origin of Mercury’s Internal Magnetic Field

A dynamo explanation for Mercury's anomalous magnetic field

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