Scale disparities and magnetohydrodynamics in the Earth’s core

Fluid motions driven by convection in the Earth’s fluid core sustain geomagnetic ­ fields by magnetohydrodynamic dynamo processes. The dynamics of the core is critically influenced by the combined effects of rotation and magnetic ­ fields. This paper attempts to illustrate the scale-related difficulties in modelling a convection-driven geodynamo by studying both linear and nonlinear convection in the presence of imposed toroidal and poloidal ­ fields. We show that there exist three extremely large disparities, as a direct consequence of small viscosity and rapid rotation of the Earth’s fluid core, in the spatial, temporal and amplitude scales of a convection-driven geodynamo. We also show that the structure and strength of convective motions, and, hence, the relevant dynamo action, are extremely sensitive to the intricate dynamical balance between the viscous, Coriolis and Lorentz forces; similarly, the structure and strength of the magnetic field generated by the dynamo process can depend very sensitively on the fluid flow. We suggest, therefore, that the zero Ekman number limit is strongly singular and that a stable convection-driven strong-­field geodynamo satisfying Taylor’s constraint may not exist. Instead, the geodynamo may vacillate between a strong ­field state, as at present, and a weak ­ field state, which is also unstable because it fails to convect sufficient heat

The effects of aliasing and lock-in processes on palaeosecular variation records from sediments

Studies of sedimentary records of palaeointensity variation report periods as long as 50 kyr. Archaeointensity data show geomagnetic periods of 2 kyr with large ampli-tudes. Sampling of the sedimentary records can be as coarse as 8 kyr, so the apparent long periods could be caused by aliasing. The sedimentary lock-in process could smooth the record and remove short periods, thereby preventing aliasing from occurring. We examine possible effects of aliasing by creating a 100-kyr-long synthetic sequence of palaeointensity variation with a similar spectrum to that of archaeomagnetic data from the last 12 kyr and resampling at longer intervals. With no lock-in smoothing,aliasing produces spurious energy in the spectra at long periods. When smoothing by the sedimentation process is applied, the amplitudes of the aliased peaks are reduced but still cause significant, spurious, long-period energy in the spectra for some sedi- mentation rates. We restrict our analysis to palaeointensity data but similar problems may also exist for coarsely sampled directional data. To avoid aliasing we recommend a maximum sampling interval of 2 kyr

Kinematic dynamo action in a sphere: Effects of periodic time-dependent flows on solutions with axial dipole symmetry

Choosing a simple class of flows, with characteristics that may be present in the Earth's core, we study the ability to generate a magnetic field when the flow is permitted to oscillate periodically in time. The flow characteristics are parameterised by D, representing a differential rotation, M, a meridional circulation, and C, a component characterising convective rolls. Dynamo action is sensitive to these flow parameters and fails spectacularly for much of the parameter space where magnetic flux is concentrated into small regions. Oscillations of the flow are introduced by varying the flow parameters in time, defining a closed orbit in the space (D,M). Time-dependence appears to smooth out flux concentrations, often enhancing dynamo action. Dynamo action can be impaired, however, when flux concentrations of opposite signs occur close together as smoothing destroys the flux by cancellation. It is possible to produce geomagnetic-type reversals by making the orbit stray into a region where the steady flows generate oscillatory fields. In this case, however, dynamo action was not found to be enhanced by the time-dependence. A novel approach is taken to solving the time-dependent eigenvalue problem, where by combining Floquet theory with a matrix-free Krylov-subspace method we avoid large memory requirements for storing the matrix required by the standard approach.Comment: 22 pages, 12 figures. Geophys. Astrophys. Fluid Dynam., as accepted (2004

Convection in the Earth's core driven by lateral variations in the core-mantle boundary heat flux

Moving core fluid maintains an isothermal core-mantle boundary (CMB), so lateral variations in the CMB heat flow result from mantle convection. Such variations will drive thermal winds, even if the top of the core is stably stratified. These flows may contribute to the magnetic secular variation and are investigated here using a simple, non-magnetic numerical model of the core. The results depend on the equatorial symmetry of the boundary heat flux variation. Large-scale equatorially symmetric (ES) heat flux variations at the outer surface of a rapidly rotating spherical shell drive deeply penetrating flows that are strongly suppressed in stratified fluid. Smaller-scale ES heat flux variations drive flows less dominated by rotation and so less inhibited by stratification. Equatorially anti-symmetric flux variations drive flows an order of magnitude less energetic than those driven by ES patterns but, due to the nature of the Coriolis force, are less suppressed by stratification. The response of the rotating core fluid to a general CMB heat flow pattern will then depend strongly on the subadiabatic temperature profile. Imposing a lateral heat flux variation linearly related to a model of seismic tomography in the lowermost mantle drives flow in a density stratified fluid that reproduces some features found in flows inverted from geomagnetic data

Dynamos with weakly convecting outer layers: implications for core-mantle boundary interaction

Convection in the Earth's core is driven much harder at the bottom than the top. This is partly because the adiabatic gradient steepens towards the top, partly because the spherical geometry means the area involved increases towards the top, and partly because compositional convection is driven by light material released at the lower boundary and remixed uniformly throughout the outer core, providing a volumetric sink of buoyancy. We have therefore investigated dynamo action of thermal convection in a Boussinesq fluid contained within a rotating spherical shell driven by a combination of bottom and internal heating or cooling. We first apply a homogeneous temperature on the outer boundary in order to explore the effects of heat sinks on dynamo action; we then impose an inhomogeneous temperature proportional to a single spherical harmonic Y2² in order to explore core-mantle interactions. With homogeneous boundary conditions and moderate Rayleigh numbers, a heat sink reduces the generated magnetic field appreciably; the magnetic Reynolds number remains high because the dominant toroidal component of flow is not reduced significantly. The dipolar structure of the field becomes more pronounced as found by other authors. Increasing the Rayleigh number yields a regime in which convection inside the tangent cylinder is strongly affected by the magnetic field. With inhomogeneous boundary conditions, a heat sink promotes boundary effects and locking of the magnetic field to boundary anomalies. We show that boundary locking is inhibited by advection of heat in the outer regions. With uniform heating, the boundary effects are only significant at low Rayleigh numbers, when dynamo action is only possible for artificially low magnetic diffusivity. With heat sinks, the boundary effects remain significant at higher Rayleigh numbers provided the convection remains weak or the fluid is stably stratified at the top. Dynamo action is driven by vigorous convection at depth while boundary thermal anomalies dominate in the upper regions. This is a likely regime for the Earth's core

Kinematic dynamo action in a sphere. II. Symmetry selection

The magnetic fields of the planets are generated by dynamo action in their electrically conducting interiors. The Earth possesses an axial dipole magnetic field but other planets have other configurations: Uranus has an equatorial dipole for example. In a previous paper we explored a two-parameter class of flows, comprising convection rolls, differential rotation (D) and meridional circulation (M), for dynamo generation of steady fields with axial dipole symmetry by solving the kinematic dynamo equations. In this paper we explore generation of the remaining three allowed symmetries: axial quadrupole, equatorial dipole and equatorial quadrupole. The results have implications for the fully nonlinear dynamical dynamo because the flows qualitatively resemble those driven by thermal convection in a rotating sphere, and the symmetries define separable solutions of the nonlinear equations. Axial dipole solutions are generally preferred (they have lower critical magnetic Reynolds number) for D > 0, corresponding to westward surface drift. Axial quadrupoles are preferred for D 0), axial dipoles are preferred. The equatorial dipole must change sign between east and west hemispheres, and is not favoured by any elongation of the flux in longitude (caused by D) or polar concentrations (caused by M): they are preferred for small D and M. Polar and equatorial concentrations can be related to dynamo waves and the sign of Parker's dynamo number. For the three-dimensional flow considered here, the sign of the dynamo number is related to the sense of spiralling of the convection rolls, which must be the same as the surface drif

Thermal and electrical conductivity of iron at Earth's core conditions

The Earth acts as a gigantic heat engine driven by decay of radiogenic isotopes and slow cooling, which gives rise to plate tectonics, volcanoes, and mountain building. Another key product is the geomagnetic field, generated in the liquid iron core by a dynamo running on heat released by cooling and freezing to grow the solid inner core, and on chemical convection due to light elements expelled from the liquid on freezing. The power supplied to the geodynamo, measured by the heat-flux across the core-mantle boundary (CMB), places constraints on Earth's evolution. Estimates of CMB heat-flux depend on properties of iron mixtures under the extreme pressure and temperature conditions in the core, most critically on the thermal and electrical conductivities. These quantities remain poorly known because of inherent difficulties in experimentation and theory. Here we use density functional theory to compute these conductivities in liquid iron mixtures at core conditions from first principles- the first directly computed values that do not rely on estimates based on extrapolations. The mixtures of Fe, O, S, and Si are taken from earlier work and fit the seismologically-determined core density and inner-core boundary density jump. We find both conductivities to be 2-3 times higher than estimates in current use. The changes are so large that core thermal histories and power requirements must be reassessed. New estimates of adiabatic heat-flux give 15-16 TW at the CMB, higher than present estimates of CMB heat-flux based on mantle convection; the top of the core must be thermally stratified and any convection in the upper core driven by chemical convection against the adverse thermal buoyancy or lateral variations in CMB heat flow. Power for the geodynamo is greatly restricted and future models of mantle evolution must incorporate a high CMB heat-flux and explain recent formation of the inner core.Comment: 11 pages including supplementary information, two figures. Scheduled to appear in Nature, April 201

Compositional instability of Earth's solid inner core

[1] All models that invoke convection to explain the observed seismic variations in Earth's inner core require unstable inner core stratification. Previous work has assumed that chemical effects are stabilizing and focused on thermal convection, but recent calculations indicate that the thermal conductivity at core temperatures and pressures is so large that the inner core must cool entirely by conduction. We examine partitioning of oxygen, sulfur, and silicon in binary iron alloys and show that inner core growth results in a variable light element concentration with time: oxygen concentration decreases, sulfur concentration decreases initially and increases later, and silicon produces a negligible effect to within the model errors. The result is a net destabilizing concentration gradient. Convective stability is measured by a Rayleigh number, which exceeds the critical value for reasonable estimates of the viscosity and diffusivity. Our results suggest that inner core convection models, including the recently proposed translational mode, can be viable candidates for explaining seismic results if the driving force is compositional

Using geomagnetic secular variation to separate remanent and induced sources of the crustal magnetic field

Magnetic fields originating from magnetized crustal rocks dominate the geomagnetic spectrum at wavelengths of 0.1-100 km. It is not known whether the magnetization is predominantly induced or remanent, and static surveys cannot discriminate between the two. Long-running magnetic observatories offer a chance, in principle, of separating the two sources because secular variation leads to a change in the main inducing field, which in turn causes a change in the induced part of the short-wavelength crustal field. We first argue that the induced crustal field, b(I)(t), is linearly related to the local core field, B(t), through a symmetric, trace-free matrix A: b(I)(t)=AB(t). We then subtract a core field model from the observatory annual means and invert the residuals for three components of the remanent field, b(R)(t), and the five independent elements of A. Applying the method to 20 European observatories, all of which have recorded for more than 50 years, shows that the most difficult task is to distinguish b(R) from the steady part of b(I). However, for nine observatories a time-dependent induced field fits the data better than a steady remanent field at the 99 per cent confidence level, suggesting the presence of a significant induced component to the magnetization

FeO Content of Earth’s Liquid Core

The standard model of Earth’s core evolution has the bulk composition set at formation, with slow cooling beneath a solid mantle providing power for geomagnetic field generation. However, controversy surrounding the incorporation of oxygen, a critical light element, and the rapid cooling rates needed to maintain the early dynamo have called this model into question. The predicted cooling rates imply early core temperatures that far exceed estimates of the lower mantle solidus, suggesting that early core evolution was governed by interaction with a molten lower mantle. Here we develop ab initio techniques to compute the chemical potentials of arbitrary solutes in solution and use them to calculate oxygen partitioning between liquid Fe-O metal and silicate melts at the pressure-temperature (P-T) conditions expected for the early core-mantle system. Our distribution coefficients are compatible with those obtained by extrapolating experimental data at lower P-T values and reveal that oxygen strongly partitions into metal at core conditions via an exothermic reaction. Our results suggest that the bulk of Earth’s core was undersaturated in oxygen compared to the FeO content of the magma ocean during the latter stages of its formation, implying the early creation of a stably stratified oxygen-enriched layer below the core-mantle boundary (CMB). FeO partitioning is accompanied by heat release due to the exothermic reaction. If the reaction occurred at the CMB, this heat sink could have significantly reduced the heat flow driving the core convection and magnetic field generation