From stable dipolar towards reversing numerical dynamos

We are using a three-dimensional convection-driven numerical dynamo model without hyperdiffusivity to study the characteristic structure and time variability of the magnetic field in dependence of the Rayleigh number (Ra) for values up to 40 times supercritical. We also compare a variety of ways to drive the convection and basically find two dynamo regimes. At low Ra, the magnetic field at the surface of the model is dominated by the non-reversing axial dipole component. At high Ra, the dipole part becomes small in comparison to higher multipole components. At transitional values of Ra, the dynamo vacillates between the dipole-dominated and the multipolar regime, which includes excursions and reversals of the dipole axis. We discuss, in particular, one model of chemically driven convection, where for a suitable value of Ra, the mean dipole moment and the temporal evolution of the magnetic field resemble the known properties of the Earth’s field from paleomagnetic data.     

A theoretical analysis of the observed variability of the geomagnetic dipole field

We present a detailed analysis of the Sint-800 virtual axial dipole moment (VADM) data in terms of an Ω mean field model of the geodynamo that features a non-steady generation of poloidal from toroidal magnetic field. The result is a variable excitation of the dipole mode and the overtones, and there are occasional dipole reversals. The model permits a theoretical evaluation of the statistical properties of the dipole mode. We show that the model correctly predicts the distribution of the VADM and the autocorrelation function inferred from the Sint-800 data. The autocorrelation technique allows us to determine the turbulent diffusion time τ_d=R²/β of the geodynamo. We find that τ_d is about 10–15 kyr. The model is able to reproduce the observed secular variation of the dipole mode, and the mean time between successive dipole reversals. On the other hand, the duration of a reversal is a factor 2 too long. This could be due to imperfections in the model or to unknown systematics in the Sint-800 data. The use of mean field theory is shown to be selfconsistent.     

A Route to Magnetic Field Reversals: An Example of an ABC-Forced Nonlinear Dynamo

We are investigating numerically the nonlinear behaviour of a space-periodic MHD system with ABC forcing. Most computations are performed for magnetic Reynolds numbers increasing from 0 to 60 and a fixed kinematic Reynolds number, small enough for the trivial solution with a zero magnetic field to be stable to velocity perturbations. At the critical magnetic Reynolds number for the onset of instability of the trivial solution the dominant eigenvalue of the kinematic dynamo problem is real. In agreement with the bifurcation theory new steady states with non-vanishing magnetic field appear in this bifurcation. Subsequent bifurcations are investigated. A regime is detected, where chaotic variations of the magnetic field orientation (analogous to magnetic field reversals) are observed in the temporal evolution of the system.     

Inner-core conductivity in numerical dynamo simulations

Speculation about its possible super-rotation has drawn the attention of many geophysical researchers to the Earth’s inner core. An issue of special interest for geodynamo modelling is the influence of the inner-core conductivity. It has been suggested that the finite magnetic diffusivity of the inner core prevents more frequent reversals of the Earth’s magnetic field. We explore the possible influence of the inner-core conductivity by comparing convection-driven 3D dynamo simulations with insulating or conducting inner cores (CIC) at various parameters. The influence on the field structure in the outer core is only marginal. The time behaviour of dipole-dominated non-reversing dynamos is also little affected. Concerning reversing dynamos, the inner-core conductivity reduces the number of short dipole-polarity intervals with a typical length of a few thousand years. Reversals are always correlated with low dipole strength and these short intervals are found in periods where the dipole moment stays low. Polarity intervals longer than about 10,000 years, where the dipole moment has time recover in strength, are equally likely in insulating and CIC models. Since these latter intervals are of more geophysical relevance, we conclude that the influence of the inner-core conductivity on Earth-like reversal sequences is insignificant for the dynamo model employed here.     

On the validity of a model for the reversals of the Earth's magnetic field

Abstract

We have used techniques of nonlinear dynamics to compare a special model for the reversals of the Earth's magnetic field with the observational data. Although this model is rather simple, there is no essential difference to the data by means of well-known characteristics, such as correlation function and probability distribution. Applying methods of symbolic dynamics we have found that the considered model is not able to describe the dynamical properties of the observed process. These significant differences are expressed by algorithmic complexity and Renyi information.     

Reversal asymmetry in Mesoproterozoic overprinting of the 1.88-Ga Gunflint Formation, Ontario, Canada: non-dipole effects or apparent polar wander?

Eighty-two palaeomagnetic samples of calcareous and jaspilitic grainstones (iron-formation or ‘taconite’) and chert carbonate were collected from the 1.88-Ga Gunflint Formation at 22 sites in the Thunder Bay area, Ontario. Twenty clasts of Gunflint taconite also were sampled from the basal conglomerate of the overlying Mesoproterozoic Sibley Group. Anisotropy of magnetic susceptibility measurements indicate the Gunflint Formation in the sampling area has not experienced regional dynamic metamorphism. Analyses by variable-field translation balance and X-ray diffraction show that the predominant magnetic mineral is hematite but a small amount of magnetite also is present in some samples. Altogether, 213 Gunflint specimens and 59 Sibley conglomerate specimens were subjected to stepwise thermal demagnetisation and 74 Gunflint specimens to stepwise alternating-frequency demagnetisation. The following components were isolated for the taconites:

• Gunflint magnetite: normal declination D=293.4°, inclination I=30.8°, α₉₅=7.2°, n=21; reverse D=86.7°, I=–54.6°, α₉₅=5.8°, n=29.

• Gunflint hematite: normal D=243.6°, I=23.6°, α₉₅=6.0°, n=11; reverse D=70.3°, I=–51.4°, α₉₅=3.2°, n=79.

• Sibley clasts magnetite: normal D=282.7°, I=33.4°, α₉₅=7.6°, n=20.

• Sibley clasts hematite: normal D=254.5°, I=56.2°, α₉₅=8.4°, n=13; reverse D=110.6°, I=–55.7°, α₉₅=8.3°, n=11.

None of these sets passed the reversal test, with the normal component generally being the shallower. Fold tests were negative or inconclusive and the conglomerate test also was negative. Chert carbonate at one other site appears to have acquired a remanence carried by magnetite (D=97.3°, I=−78.2°, α₉₅=6.3°, n=18) prior to folding related to Keweenawan (1.1 Ga) Logan diabase sill emplacement. Most of the components we identified match components for Keweenawan sills, volcanic rocks, intrusions and baked contact rocks in the Thunder Bay area, indicating that Keweenawan magmatism caused widespread chemical remagnetisation of the Proterozoic country rock in our sampling area. Although others have argued that asymmetry was a feature of the Keweenawan geomagnetic field, the declinations of our Gunflint and Sibley hematite and magnetite components are different, suggesting that the components were acquired at significantly different times. We conclude that the reversal asymmetry shown by our Gunflint and Sibley data may best be ascribed to apparent polar wander during Keweenawan times.     

The magnetic structure of convection-driven numerical dynamos

The generation of a magnetic field in numerical simulations of the geodynamo is an intrinsically 3-D and time-dependent phenomenon. The concept of magnetic field lines and the frozen-flux approximation can provide insight into such systems, but a suitable visualization method is required. This paper presents results obtained using the Dynamical Magnetic Field line Imaging (DMFI) technique, which is a representation of magnetic field lines accounting for their local magnetic energy, together with an algorithm for the time evolution of their anchor points. The DMFI illustrations are consistent with previously published dynamo mechanisms, and allow further investigation of spatially and temporally complex systems. We highlight three types of magnetic structures: (i) magnetic cyclones and (ii) magnetic anticyclones are expelled by, but corotate with axial flow vortices; (iii) magnetic upwellings are amplified by stretching and advection within flow upwellings, and show structural similarity with helical plumes found in rotating hydrodynamic experiments. While magnetic anticyclones are responsible for the regeneration of a stable axial dipole, here we show that excursions and reversals of the dipole axis are caused by the emergence of magnetic upwellings, which amplify and transport a generally multipolar magnetic field from the inner to the outer boundary of the models. Geomagnetic observations suggest the presence of magnetic structures similar to those found in our models; thus, we discuss how our results may pertain to Earth's core dynamo processes. In order to make DMFI a standard tool for numerical dynamo studies, a public software package is available upon request to the authors (supplementary material is available at: http://www.ipgp.jussieu.fr/~aubert/DMFI.html ).     

The geodynamo as a bistable oscillator

Abstract

Our intent is to provide a simple and quantitative understanding of the variability of the axial dipole component of the geomagnetic field on both short and long time scales. To this end we study the statistical properties of a prototype nonlinear mean field model. An azimuthal average is employed, so that (1) we address only the axisymmetric component of the field, and (2) the dynamo parameters have a random component that fluctuates on the (fast) eddy turnover time scale. Numerical solutions with a rapidly fluctuating α reproduce several features of the geomagnetic field: (1) a variable, dominantly dipolar field with additional fine structure due to excited overtones, and sudden reversals during which the field becomes almost quadrupolar, (2) aborted reversals and excursions, (3) intervals between reversals having a Poisson distribution. These properties are robust, and appear regardless of the type of nonlinearity and the model parameters. A technique is presented for analysing the statistical properties of dynamo models of this type. The Fokker-Planck equation for the amplitude a of the fundamental dipole mode shows that a behaves as the position of a heavily damped particle in a bistable potential ∝(1 ? a ²)², subject to random forcing. The dipole amplitude oscillates near the bottom of one well and makes occasional jumps to the other. These reversals are induced solely by the overtones. Theoretical expressions are derived for the statistical distribution of the dipole amplitude, the variance of the dipole amplitude between reversals, and the mean reversal rate. The model explains why the reversal rate increases with increasing secular variation, as observed. Moreover, the present reversal rate of the geodynamo, once per (2?3) × 10⁵ year, is shown to imply a secular variation of the axial dipole moment of ～ 15% (about the current value). The theoretical dipole amplitude distribution agrees well with the Sint-800 data.