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Recent theory and experiment suggest the thermal and electrical conductivities of the Earth’s core are 2–4 times higher than previously thought. This has important consequences for the core’s thermal history and behaviour of the geodynamo. The conductivities increase with depth, with a discontinuous jump at the inner core boundary caused by the change in composition and phase change to a solid. Properties of putative core alloys are now sufficiently well known to make it worth exploring the effects of their variation with depth within the core. The magnetic decay times are increased to 58 kyr for the whole core, considerably longer than the advection time (the time it takes fluid to traverse the outer core), and 9 kyr for the solid inner core. Heat conducted down the adiabat through the core–mantle boundary is in excess of 15 TW, which is one third of the Earth’s total heat loss and 2–3 times higher than most estimates. The core can be stirred by chemical convection against a stable thermal gradient, but at a cost that reduces the effective power available for generating magnetic field. We estimate the minimum heat flux required to sustain thermal dissipation alone to be 5–8 TW, but this is almost certainly a gross underestimate because it leaves nothing for convective or dynamo processes. Conduction gradients for cooling rates corresponding to these minimum heat fluxes are subadiabatic in the top 740 km of the core, which is also unlikely because geomagnetic secular variation requires upwelling somewhere near the core surface. Lateral variations in heat flux at the core–mantle boundary could easily be large enough to exceed the adiabatic value in some places, leading to mixing throughout the upper core. This not only reduces the total heat flux required to produce a well-mixed core, but also explains how mantle anomalies can exert a strong influence on core convection and the form of the geomagnetic field at the core surface. We propose a model of core convection that is vigorous in the lower part and very weak in the upper part. [ABSTRACT FROM AUTHOR]

The problem of understanding how Earth's magnetic field is generated is one of the foremost challenges in modern science. It is believed to be generated by a dynamo process, where the complex motions of an electrically conducting fluid provide the inductive action to sustain the field against the effects of dissipation. Current dynamo simulations, based on the numerical approximation to the governing equations of magnetohydrodynamics, cannot reach the very rapid rotation rates and low viscosities (i.e. low Ekman number) of Earth due to limitations in available computing power. Using a pseudospectral method, the most widely used method for simulating the geodynamo, computational requirements needed to run simulations in an 'Earth-like' parameter regime are explored theoretically by approximating operation counts, memory requirements and communication costs in the asymptotic limit of large problem size. Theoretical scalings are tested using numerical calculations. For asymptotically large problems the spherical transform is shown to be the limiting step within the pseudospectral method; memory requirements and communication costs are asymptotically negligible. Another limitation comes from the parallel implementation, however, this is unlikely to be threatened soon and we conclude that the pseudospectral method will remain competitive for the next decade. Extrapolating numerical results based upon the code analysis shows that simulating a problem characterizing the Earth with Ekman number E = 10 would require at least 13 000 days per magnetic diffusion time with 54 000 available processors, a formidable computational challenge. At E = 10 an allocation of around 350 million CPU hours would compute a single diffusion time, many more CPU hours than are available in current supercomputing allocations but potentially reachable in the next decade. Exploration of the 10⩽ E⩽10 regime could be performed at the present time using a substantial share of national supercomputing facilities or a dedicated cluster. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We model the inner core by an alloy of iron and 8 per cent sulphur or silicon and the outer core by the same mix with an additional 8 per cent oxygen. This composition matches the densities of seismic model, Preliminary Reference Earth Model (PREM). When the liquid core freezes S and Si remain with the Fe to form the solid and excess O is ejected into the liquid. Properties of Fe, diffusion constants for S, Si, O and chemical potentials are calculated by first-principles methods under the assumption that S, O, and Si react with the Fe and themselves, however, not with each other. This gives the parameters required to calculate the power supply to the geodynamo as the Earth's core cools. Compositional convection, driven by light O released at the inner-core boundary on freezing, accounts for half the entropy balance and 15 per cent of the heat balance. This means the same magnetic field can be generated with approximately half the heat throughput needed if the geodynamo were driven by heat alone. Chemical effects are significant: heat absorbed by disassociation of Fe and O almost nullify the effect of latent heat of freezing in driving the dynamo. Cooling rates below 69 K Gyr−1 are too low to maintain thermal convection everywhere; when the cooling rate lies between 35 and 69 K Gyr−1 convection at the top of the core is maintained compositionally against a stabilizing temperature gradient; below 35 K Gyr−1 the dynamo fails completely. All cooling rates freeze the inner core in less than 1.2 Gyr, in agreement with other recent calculations. The presence of radioactive heating will extend the life of the inner core, however, it requires a high heat flux across the core–mantle boundary. Heating is dominated by radioactivity when the inner core age is 3.5 Gyr. We, also, give calculations for larger concentrations of O in the outer core suggested by a recent estimation of the density jump at the inner-core boundary, which is larger than that of PREM. Compositional convection is enhanced for the higher density jumps and overall heat flux is reduced for the same dynamo dissipation, however, not by enough to alter the qualitative conclusions based on PREM. Our preferred model has the core convecting near the limit of thermal stability, an inner-core age of 3.5 Gyr and a core heat flux of 9 TW or 20 per cent of the Earth's surface heat flux, 80 per cent of which originates from radioactive heating. [ABSTRACT FROM AUTHOR]

Roughly 30 years have passed since the last publication of a linear resolution calculation of density inside the Earth. Since that time, the data set of free oscillation degnerate frequencies has been completely re-estimated taking into account the biassing effects of splitting and coupling due to 3D structure. This paper presents a new resolution analysis based on the new data and focuses on two particular issues: (1) the density jump at the inner-core boundary which is important in discussions of the maintenance of the geodynamo; and (2) a possible density excess in the lowermost mantle which might be indicative of a “hot abyssal layer”. We find that the density jump at the inner-core boundary is 0.82±0.18 Mg m−3 which is significantly larger than previously thought. We also find little support for an excess density in the lowermost mantle though an increase of 0.4% is possible. [Copyright &y& Elsevier]

The power required to drive the geodynamo places significant constraints on the heat passing across the core–mantle boundary and the Earth's thermal history. Calculations to date have been limited by inaccuracies in the properties of liquid iron mixtures at core pressures and temperatures. Here we re-examine the problem of core energetics in the light of new first-principles calculations for the properties of liquid iron. There is disagreement on the fate of gravitational energy released by contraction on cooling. We show that only a small fraction of this energy, that associated with heating resulting from changes in pressure, is available to drive convection and the dynamo. This leaves two very simple equations in the cooling rate and radioactive heating, one yielding the heat flux out of the core and the other the entropy gain of electrical and thermal dissipation, the two main dissipative processes. This paper is restricted to thermal convection in a pure iron core; compositional convection in a liquid iron mixture is considered in a companion paper. We show that heat sources alone are unlikely to be adequate to power the geodynamo because they require a rapid secular cooling rate, which implies a very young inner core, or a combination of cooling and substantial radioactive heating, which requires a very large heat flux across the core–mantle boundary. A simple calculation with no inner core shows even higher heat fluxes are required in the absence of latent heat before the inner core formed. [ABSTRACT FROM AUTHOR]

Evaluates the intrinsic stability of the geodynamo process. Excursions of the geomagnetic field in paleomagnetic studies; Domination of an axial dipole in the normal state of the geomagnetic field; Imposition of magnetic field with both toroidal and poloidal components.

Abstract: We report on the thermal and electrical conductivities of solid iron and iron–silicon mixtures (Fe0.92Si0.08 and Fe0.93Si0.07), representative of the composition of the Earth's solid inner core at the relevant pressure–temperature conditions, obtained from density functional theory calculations with the Kubo–Greenwood formulation. We find thermal conductivities , and electrical conductivities at the top of the inner core (centre of the Earth). These values are respectively about 45–56% and 18–25% higher than the corresponding conductivities in the liquid outer core. The higher conductivities are due to the solid structure and to the lower concentration of light impurities. These values are much higher than those in use for previous inner core studies, k by a factor of four and σ by a factor of three. The high thermal conductivity means that heat leaks out by conduction almost as quickly as the inner core forms, making thermal convection unlikely. The high electrical conductivity increases the magnetic decay time of the inner core by a factor of more than three, lengthening the magnetic diffusion time to 10 kyr and making it more likely that the inner core stabilises the geodynamo and reduces the frequency of reversals. [Copyright &y& Elsevier]

Highlights • Spectral methods are applied to products of dynamo simulations. • Dipole energy at the surface linked with magnetic energy in the core at long period. • Skewed magnetic dipole growth and decay linked to induction and dissipation. • Transition from low frequency steady state to higher frequency dynamo operation. • Variations in diffusion linked to changes in field strength rather than lengthscale. Abstract The geomagnetic field displays complicated variations over a broad range of frequencies. These variations can be decomposed by frequency and linked to physical processes using frequency domain spectral methods. These spectral methods are well developed but have not previously been applied to study the energy balance of geodynamo simulations. We illustrate their potential by analyzing output from numerical dynamo simulations that have previously been studied for their apparently Earth-like properties. We show that high coherence between variations in axial dipole energy at the outer boundary of the simulation and total magnetic energy within the fluid shell occur at frequencies below ∼0.1 kyr−1. This suggests that paleomagnetically-observable signals with periods exceeding 10 kyrs contain information about magnetic energy changes in the bulk core. We then use spectral analysis to investigate differences in the rate of growth and decay of the axial dipole field. This behaviour, characterised by rapid growth and slow decay, is observed when signals with frequencies higher than 0.03 kyr−1 have been filtered out. The origin of this asymmetric growth and decay is assessed using coherence spectra between rates of change in kinetic and magnetic energy, ohmic and viscous dissipation, and work done by the buoyancy and Lorentz forces. We show that asymmetry is associated with an imbalance between ohmic dissipation and work done by the Lorentz force; when changes in magnetic energy are more coherent with ohmic dissipation the field grows rapidly and decay slowly. Variations in Ohmic dissipation reflect changes in field strength in our models, while changes in viscous dissipation are associated with amplitude fluctuations of the large-scale flow that exists on millennial timescales. Our work shows that spectral analysis coupling observable and global products of the dynamo process can elucidate the physical origin of periodic processes occurring on timescales exceeding 10 kyrs. [ABSTRACT FROM AUTHOR]