Rotating convection-driven dynamos at low Ekman number

Rotvig, Jon; Jones, Chris

doi:10.1103/physreve.66.056308

Cited by 66 publications

(58 citation statements)

References 14 publications

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“…The change in flow length scale and the runaway growth have also been observed in simplified selfconsistent dynamo simulations that employ Cartesian geometries (Rotvig and Jones 2002;Stellmach and Hansen 2004). These simulations suggest that the Ekman number has to be small enough for these effects to be significant, probably as low as E ≤ 10 −5 (Stellmach and Hansen 2004).…”

Section: Flow Structurementioning

confidence: 79%

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: Flow Structurementioning

confidence: 79%

Theory and Modeling of Planetary Dynamos

Wicht

Tilgner

2010

Space Sci Rev

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“…Brandenburg 2001Brandenburg , 2005aBrandenburg et al 2001;Mininni et al 2005;Brandenburg & Käpylä 2007;Yousef et al 2008a,b;) and dynamos driven by the magnetorotational instability exhibit large-scale dynamos (e.g. Brandenburg et al 1995;Hawley et al 1996), convection simulations have not been able to produce appreciable large-scale magnetic fields until recently (Rotvig & Jones 2002;Browning et al 2006;Brown et al 2007;Käpylä et al 2008, hereafter Paper I;Hughes & Proctor 2009). The main ingredient missing in many earlier simulations was a large-scale shear flow and boundary conditions which allow magnetic helicity fluxes out of the system.…”

Section: Introductionmentioning

confidence: 99%

Alpha effect and turbulent diffusion from convection

Käpylä¹,

Korpi²,

Brandenburg

2009

A&A

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Aims. We study turbulent transport coefficients that describe the evolution of large-scale magnetic fields in turbulent convection. Methods. We use the test field method, together with three-dimensional numerical simulations of turbulent convection with shear and rotation, to compute turbulent transport coefficients describing the evolution of large-scale magnetic fields in mean-field theory in the kinematic regime. We employ one-dimensional mean-field models with the derived turbulent transport coefficients to examine whether they give results that are compatible with direct simulations. Results. The results for the α-effect as a function of rotation rate are consistent with earlier numerical studies, i.e. increasing magnitude as rotation increases and approximately cos θ latitude profile for moderate rotation. Turbulent diffusivity, η t , is proportional to the square of the turbulent vertical velocity in all cases. Whereas η t decreases approximately inversely proportional to the wavenumber of the field, the α-effect and turbulent pumping show a more complex behaviour with partial or full sign changes and the magnitude staying roughly constant. In the presence of shear and no rotation, a weak α-effect is induced which does not seem to show any consistent trend as a function of shear rate. Provided that the shear is large enough, this small α-effect is able to excite a dynamo in the mean-field model. The coefficient responsible for driving the shear-current effect shows several sign changes as a function of depth but is also able to contribute to dynamo action in the mean-field model. The growth rates in these cases are, however, well below those in direct simulations, suggesting that an incoherent α-shear dynamo may also act in the simulations. If both rotation and shear are present, the α-effect is more pronounced. At the same time, the combination of the shear-current and Ω × J-effects is also stronger than in the case of shear alone, but subdominant to the α-shear dynamo. The results of direct simulations are consistent with mean-field models where all of these effects are taken into account without the need to invoke incoherent effects.

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“…The Lorentz force itself allows the flow to gain the strength necessary for the dynamo process and also increases the length scale of the flow, two effects that have been identified in dynamo simulations in Cartesian geometry (Rotvig and Jones 2002;Stellmach and Hansen 2004). However, these effects have not been found in the spherical-shell simulations that so successfully explain the geomagnetic field (Christensen and Aubert 2006), even though the Lorentz force indeed balances the Coriolis force to a good degree (Aubert 2005).…”

Section: Mercury's Elsasser Numbermentioning

confidence: 80%

The Origin of Mercury’s Internal Magnetic Field

et al. 2007

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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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Rotating convection-driven dynamos at low Ekman number

Cited by 66 publications

References 14 publications

Theory and Modeling of Planetary Dynamos

Theory and Modeling of Planetary Dynamos

Alpha effect and turbulent diffusion from convection

The Origin of Mercury’s Internal Magnetic Field

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