Energy geodynamo parameters compatible with analytical,numerical, paleomagnetic models and observations

A hydromagnetic dynamo is only possible at a sufficiently powerful convection. In the Earth’s core, it is probably the nonthermal convection very much in excess of its critical level with the molecular transporr coefficients. However, in the case of medium- or large-scale fields, the critical energy level caused by the turbulent tranport coefficients is likely to be slightly below the actual level. This probably explains both the 22-year success of this type of simplified geodynamo models and the energy scaling laws for hydromagnetic fields, which generalize these models. Also the review of energy-dependent analytical and observational estimates of vortex fields, hydromagnetic scale sizes, and velocities in the core is presented. These typical parameters are partly in a new way linked to the observed and more ancient magnetic variations. New, albeit, simplified and self-evident, substantiation is given to the paleomagnetic hypothesis about the predominance of the axial dipole under a certain time averaging. In (Pozzo et al., 2012) and more recent works, it is shown that the adiabatic heat flow and electrical conductivity in the Earth’s core are severalfold higher than the generally accepted estimates. Here, the dynamo supporting Braginsky’s convection (Braginsky, 1963) (under the crystallization of the heavy fraction of a liquid onto the solid core) started less than 1 Ga ago, whereas the more ancient geodynamo was supported by the compositional convection of another type. The known mechanisms implementing this convection, which differ by the scenarios of magnetic evolution, are reviewed. This may help identify the sought mechanism through the most ancient paleomagnetic estimates of the field’s intensity and through the numerical models. The probable mechanisms of generation and their absence for the primordial and recent magnetic field of the studied terrestrial planets are discussed.     

Anisotropic turbulent thermal diffusion and thermal convection in a rapidly rotating fluid sphere

Estimates of the molecular values of magnetic, viscous and thermal diffusion suggest that the state of the Earth’s core is turbulent and that complete numerical simulation of the geodynamo is not realizable at present. Large eddy simulation of the geodynamo with modelling of the sub-grid scale turbulence must be used. Current geodynamo models effectively model the sub-grid scale turbulence with isotropic diffusivities larger than the molecular values appropriate for the core. In the Braginsky and Meytlis (1990) picture of core turbulence the thermal and viscous diffusivities are enhanced up to the molecular magnetic diffusivity in the directions of the rotation axis and mean magnetic field. We neglect the mean magnetic field herein to isolate the effects of anisotropic thermal diffusion, enhanced or diminished along the rotation axis, and explore the instability of a steady conductive basic state with zero mean flow in the Boussinesq approximation. This state is found to be more stable (less stable) as the thermal diffusion parallel to the rotation axis is increased (decreased), if the transverse thermal diffusion is fixed. To examine the effect of simultaneously varying the diffusion along and transverse to the rotation axis, the Frobenius norm is used to control for the total thermal diffusion. When the Frobenius norm of the thermal diffusion tensor is fixed, it is found that increasing the thermal diffusion parallel to the rotation axis is destabilising. This result suggests that, for a fixed total thermal diffusion, geodynamo codes with anisotropic thermal diffusion may operate at lower modified Rayleigh numbers.     

Certain spectral properties of cyclonic turbulence in the Earth’s liquid core

Rapid diurnal rotation of planets results in the appearance of cyclonic thermal turbulence in liquid cores, which is the source of generation of the observed magnetic fields. The model that makes it possible to reproduce characteristic features of small-scale geostrophic flows in the physical and wave spaces is considered in the work. The flows of energy and hydrodynamic helicity as a function of the wavenumber have been estimated. Joint existence of direct and inverse cascades has been indicated. The consequences for the Earth’s core and geodynamo problems have been considered.     

Towards a realistic theory of the geodynamo

Abstract

The physics of the geodynamo is discussed. The main processes relevant for the buoyancy driven geodynamo are isolated. The successive stages of development of geodynamo theory are briefly described. The mechanism of local turbulence in the Earth's core is explained, and an estimate is presented of the turbulent transport of density inhomogeneities in the Earth's core. The significance of this turbulent transport to the geodynamo mechanism is stressed. The general scheme of the complete geodynamo theory of the future is outlined.     

On the modified Taylor constraint

A dynamo driven by motions unaffected by viscous forces is termed magnetostrophic. Although such a model might describe magnetic field generation in Earth’s core well, a magnetostrophic dynamo has not yet been found even though Taylor [Proc. R. Soc. Lond. A 1963, 274, 274–283] devised an apparently viable method of finding one. His method for determining the fluid velocity from the magnetic field and the energy source involved only the evaluation of integrals along lines parallel to the Earth’s axis of rotation and the solution of a second-order ordinary differential equation. It is demonstrated below that an approximate solution of this equation for a broad family of magnetic fields is immediate. Furthermore inertia, which was neglected in Taylor’s theory, is restored here, so that the modified theory includes torsional waves, whose existence in the Earth’s core has been inferred from observations of the length of day. Their theory is reconsidered.     

The geodynamo,past, present and future

Abstract

The geodynamo simulation of Glatzmaier and Roberts (1996, Physica D97, 81) is driven by the cooling of the model Earth, which releases latent heat and light components of core fluid at the freezing surface of the inner core as it advances outwards. At some time in the past, the inner core was only a quarter of its present size and at some time in the future it will be twice its present size. The geodynamo operating during those epochs are studied here, the three models (past, present and future) being tied together in an evolutionary sense. The time taken for the models to evolve from past to future depends on the cooling rate, which is controlled by the dynamics of the mantle and is not studied here. All three models generate external fields of comparable strength and all three appear to be close to Taylor states. Unexpectedly, the future model showed considerable variability in time, while the past model does not. Deviations from axisymmetry in the external field increase with inner core radius and the relative predominance of the centered dipole over other multipole components declines.     

Magnetorotational instability in the Earth’s core

The anisotropy of the convection in the Earth’s core can act as a cause of its nonsolid rotation. In the case of differential rotation, the magneto-rotational instability (the Velikhov instability) can arise in the liquid core. It is shown that the development of the magneto-rotational instability of the hydromagnetic flows in the liquid core of the Earth can generate variations in the geomagnetic field observed on the Earth’s surface.     

Energetic scaling of the geodynamo

The typical scales, velocities, and magnetic fields in the liquid core of the Earth are determined by using the analysis results of the magnitude of energy that is available for the geodynamo, physical regularities, and observational data. In this work, it is justified that the geomagnetic field is mainly generated in a regime where the magnetic Lorentz force is equilibrated by the Archimedean buoyancy force and by the Coriolis rotational force and the force of inertia is considerably less than these forces. The characteristic periods obtained in the course of this justification permit one to clarify not only the physical nature of secular geomagnetic variations but also that of jerks. In another regime, which is less probable for the present-day Earth, the main balance of forces is determined by inertia and buoyancy; the magnetic field has no significant effect on the typical rate and scale of convection. This regime seems to be probable in the liquid core of the Earth during inversions or digressions, as well as in depths of Mercury, Mars, Uranus, and Neptune.     

On the frequency variations in the Earth’s rotation caused by unstable flows in the liquid core

The correlation between frequency variations in the Earth’s rotation and geomagnetic jerks is analyzed on the interval from 1900 to 2008. It is found that jerks precede changes in the rate of the Earth’s rotation frequency in the interval of periods ranging from 5 to 8 years. A mechanism of jerks generation is suggested in which the jerks are considered as the result of the excitation of magnetorotational instability in the Earth’s core with the subsequent generation of torsional oscillations causing a change in the Earth’s rotation frequency.     

Torque balance and energy budget for the precessionally driven dynamo

The feasibility of a precessionally driven dynamo is investigated. The relative orientation of the angular-velocity vectors of the mantle and core and the precession vector of the earth are determined from a torque balance. The core and mantle are acted upon by separate gravitational torques and mutual interaction torques resulting from pressure, viscous and magnetic stresses at the core-mantle interface. The viscous and magnetic torques are determined using the results of a detailed analysis of the Ekman-Hartmann and magnetic diffusion layers generated at the core-mantle interface by the misalignment of the mantle and core angular-velocity vectors. The dissipative torques are found to be weaker by a factor of 10^?4 than those estimated by Malkus (1968) and Stacey (1973), resulting in only 3.5 · 10⁷ W being extracted from the rotational kinetic energy of the earth by these mechanisms. Furthermore, it is found that all of this energy is dissipated in the boundary layers at the core-mantle interface and none is available to drive the geodynamo.     

Mean-field concept and direct numerical simulations of rotating magnetoconvection and the geodynamo

Mean-field theory describes magnetohydrodynamic processes leading to large-scale magnetic fields in various cosmic objects. In this study magnetoconvection and dynamo processes in a rotating spherical shell are considered. Mean fields are defined by azimuthal averaging. In the framework of mean-field theory, the coefficients which determine the traditional representation of the mean electromotive force, including derivatives of the mean magnetic field up to the first order, are crucial for analyzing and simulating dynamo action. Two methods are developed to extract mean-field coefficients from direct numerical simulations of the mentioned processes. While the first method does not use intrinsic approximations, the second one is based on the second-order correlation approximation. There is satisfying agreement of the results of both methods for sufficiently slow fluid motions. Both methods are applied to simulations of rotating magnetoconvection and a quasi-stationary geodynamo. The mean-field induction effects described by these coefficients, e.g., the α-effect, are highly anisotropic in both examples. An α²-mechanism is suggested along with a strong γ-effect operating outside the inner core tangent cylinder. The turbulent diffusivity exceeds the molecular one by at least one order of magnitude in the geodynamo example. With the aim to compare mean-field simulations with corresponding direct numerical simulations, a two-dimensional mean-field model involving all previously determined mean-field coefficients was constructed. Various tests with different sets of mean-field coefficients reveal their action and significance. In the magnetoconvection and geodynamo examples considered here, the match between direct numerical simulations and mean-field simulations is only satisfying if a large number of mean-field coefficients are involved. In the magnetoconvection example, the azimuthally averaged magnetic field resulting from the numerical simulation is in good agreement with its counterpart in the mean-field model. However, this match is not completely satisfactory in the geodynamo case anymore. Here the traditional representation of the mean electromotive force ignoring higher than first-order spatial derivatives of the mean magnetic field is no longer a good approximation.     

Estimation of Free Core Resonance Parameters Based on Long-Term Strain Observations in the Diurnal Frequency Band

Izvestiya, Physics of the Solid Earth - The free core nutation (FCN) is one of the Earth’s rotational eigenmodes, which is caused by the retrograde motion of the liquid core relative to the...     

Energy cycle of geodynamics and the seismic process

Estimates are obtained for the energy cycle of geodynamics, namely, the contributions of the geothermal flux to the generation rate of the kinetic energy of convective motions in the mantle and the generation of stresses in the crust that are later released during earthquakes. As follows from theoretical considerations, about half of the geothermal flux is spent on the generation of motions in the mantle, and the fraction of the total geothermal flux from the Earth’s interior that is spent on the seismic process is estimated at 0.5%. This estimate is obtained with the use of data of global earthquake catalogs. For volcanic processes, this fraction is smaller by two orders of magnitude. The energies required for the formation of the Earth’s surface topography and for seismic activity are comparable.     

Ground Geophysical Surveys: Measuring Tools

The paper considers some original strainmeters and gravitoinertial instruments designed at the Schmidt Institute of Physics of the Earth, Russian Academy of Sciences. The instruments are successfully used for measuring the Earth’s gravitational field, tilts, and deformations of the Earth’s crust in solving a number of applied and fundamental problems in geophysics and geodynamics, in particular, evaluating and monitoring the stability of environmentally hazardous engineering and construction objects (dams, hydroelectric dams, nuclear power plants, oil and gas pipelines, etc.), searching for the zones of weakness in the Earth’s crust, identifying precursors of natural and technological disasters, studying the Earth’s global characteristics (lunar–solar tides, irregularity of the Earth’s rotation, translational oscillations of the Earth’s core, and azimuthal shifts of lithosphere blocks).     

Lunar–solar tide effects in the Earth’s crust and atmosphere

The gravitational interaction in the Earth–Moon–Sun system is considered from the standpoint of influencing the formation of time variations in the geophysical fields and some natural processes. The analysis of the results of instrumental observations revealed the main periodicities and cycles in the time variations of subsoil radon volumetric activity with the same periods as the vertical component of the variations of the tidal force. The amplitude modulation of seismic noise by the lunar-solar tide is demonstrated. It is shown that the intensity of relaxation processes in the Earth’s crust has a near-diurnal periodicity, whereas the spectrum of groundwater level fluctuations includes clearly expressed tidal waves. Based on the data on the tilts of the Earth’s surface, the role of tidal deformation in the formation of the block motions in the Earth’s crust is analyzed. A new approach is suggested for identifying tidal waves in the atmosphere by analyzing micropulsations of the atmospheric pressure with the use of adaptive rejection filters.     

Local turbulence in the Earth's core

Abstract

It is shown that in the Earth's core, where the geodynamo is at work (and is supplied with energy by the prevailing unstable density stratification), a buoyancy instability of a local character exists which is highly supercritical. This instability results in fully developed turbulence dominated by small scale vortices. The influence of the Earth's rotation and of the magnetic field produced by the geodynamo makes this small scale turbulence highly anisotropic. A qualitative picture of this local anisotropic turbulence is devised and the main parameters characterizing it are estimated. Expressions for the turbulent diffusivity are developed and discussed.     

The effects of different parameter regimes in geodynamo simulations

Over the past 10 years, geodynamo simulations have grown rapidly in sophistication. However, it is still necessary to make certain approximations in order to maintain numerical stability. In addition, models are forced to make assumptions about poorly known parameters for the Earth's core. Different magnetic Prandtl numbers have been used and different assumptions about the presence of radiogenic heating have been made. This study examines some of the consequences of different approximations and assumptions using the Glatzmaier–Roberts geodynamo model. Here, we show that the choice of magnetic Prandtl number has a greater influence on the character of the magnetic field produced than the addition of a plausible amount of radiogenic heating. In particular, we find that prescribing a magnetic Prandtl number of unity with Ekman number limited by current computing resources, results in magnetic fields with significantly smaller intensities and variabilities compared with the much more Earth-like results obtained from simulations with large magnetic Prandtl numbers. A magnetic Prandtl number of unity, with both the viscous and magnetic diffusivities set to the Earth's magnetic diffusivity, requires a rotation rate much smaller than that of the Earth for currently reachable Ekman numbers. This results in a reduced dominance of the Coriolis forces relative to the buoyancy forces, and therefore, a reduction in the magnetic field intensity and the variability compared to the large Prandtl number cases.     

Structure of the inner core boundary

Abstract

A model of the inner-core boundary (ICB) is constructed which is consistent with current ideas of the dynamic and thermodynamic state of the core and which is capable of reflecting seismic waves with period of one second. This requires the mass fraction of solid below the ICB to grow to an appreciable fraction in roughly one kilometer. This rapid growth of solid with depth is a result of downward fluid flow from the outer core which is a part of the convective motions which sustain the geodynamo. The solid which crystallizes from this descending fluid after it crosses the ICB continually coats the dendrites which occur there. The gradual cooling of the outer core causes the ICB to advance by growth of dendrites at their tips. The balance of these two effects gives an equilibrium profile for the mass fraction of solid with depth below the ICB which is capable of yielding sharp reflection of seismic waves.     

Tidal components of geomagnetic variations

The natural geomagnetic field is constantly disturbed. The total registered effect of geomagnetic variations depends on both planetary and local processes. Planetary sources and sources in the Earth’s core respond to tidal effects. In the accepted model, the complex MHD processes in the Earth’s outer core are approximated by the assumed ring current in the equatorial plain of the liquid core. The geomagnetic variation originating as a result of tidal deformations of ring currents are ～10^?4 and 0.10–1 nT in the liquid core and magnetosphere, respectively. The calculated values coincide in order of magnitude with the processed geomagnetic measurements at Paratunka observatory (Kamchatka region).