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 precession driven geodynamo

Formation of flow structures in the Earth’s liquid core enclosed in a precessing and rotating shell (mantle) is examined within the hydrodynamic approach. The kinematics and energetics of the motions in the Earth’s core initiated by precession allow one to regard these motions as a possible geodynamo mechanism at an early evolutionary stage of the Earth (prior to the formation of the solid core). The influence of the precession driven geodynamo on the stability of the geomagnetic field is discussed.     

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.     

Three-dimensional domino model in geodynamo

The Lagrangian formalism is applied to consider temporal evolution of the ensemble of interacting magnetohydrodynamical cyclones governed by Langevin-type equations in a rotating medium. This problem is relevant for fast-rotating convective objects such as the cores of planets and a number of stars, where the Rossby numbers are far below unity and the geostrophic balance of the forces takes place. The paper presents the results of modeling for both the two-dimensional (2D) case when the cyclones can rotate relative to the rotation axis of the whole system in the vertical plane, and for the case of spatial rotation by two angles. It is shown that variations in the heat flux on the outer boundary of the spherical shell modulate the frequency of the reversals of the mean dipole magnetic field, which agrees with the three-dimensional (3D) modeling of the planetary dynamo. Applications of the model for giant planets are discussed, and an explanation for some episodes in the history of the geomagnetic field in the past is suggested.     

Hydrodynamic helicity in Boussinesq-type models of the geodynamo

The generation of hydrodynamic helicity is considered in models of thermal convection of a rapidly rotating incompressible liquid (small Rossby numbers). It is shown that a system of cyclonic vortices arising in geodynamo models generates a large-scale hydrodynamic helicity. The spatial distribution of the helicity is analyzed as a function of the intensity of heat sources in models with various boundary conditions for the velocity field.     

On the role of magnetostrophic waves in geodynamo

It is shown that magnetostrophic waves which are generated in the equatorial plane of the Earth’s core due to the instability of the equatorial jet and which propagate almost transversely to the rotational axis off the tangent cylinder, have a negative helicity in the northern hemisphere and positive helicity in the southern hemisphere. When the wave trains propagate through the regions with a constant azimuthal magnetic field caused by the Ω-effect, this helicity distribution induces an electromotive force (emf) (due to the α-effect), which may lead to the maintenance of the initial dipole field by the scenario of the α-Ω dynamo.     

Tuning of the mean-field geodynamo model

Parker’s two-dimensional (2D) dynamo model with an algebraic form of nonlinearity for the α-effect is considered. The model uses geostrophic distributions for the α-effect and differential rotation, which are derived from the three-dimensional (3D) convection models. The resulting configurations of the magnetic field in the liquid core are close to the solutions in Braginsky’s Z-model. The implications of the degree of geostrophy observed in the 3D dynamo models for the behavior of the mean magnetic field are explored. It is shown that the reduction in geostrophy leads to magnetic field reversals accompanied by the relative growth of the nondipole component of the field on the surface of the liquid core. The simulations with a random α-effect which causes turbulent pulsations are carried out. The approach is capable of producing realistic sequences of magnetic reversals.     

Geomagnetic reversals in a simple geodynamo model

A simple finite-dimensional geodynamo model, obtained from the equations of the mean field electrodynamics and reproducing the phenomenon of geomagnetic reversals, is proposed. It has been indicated that the reversal scale obtained in the scope of this model is rather close to the observed scale in its properties. The reversal mechanism is related to the α-effect fluctuations. It is not necessary to substantially change the hydrodynamic parameters of the problem so that a reversal originates in the scope of such a model, but it is only sufficient to take the α-effect fluctuations into account. If the rms deviation of fluctuations accounts for 10% of the average α value, a fluctuation of two-three standard deviations is sufficient for the origination of a reversal, which quite agrees with the concept that reversals are rather rare phenomena. Another factor resulting in the regime with reversals is that the model can generate magnetic fields with different behaviors in different regions of the parametric space in linear mode: monotonically increasing fields and fields increasing with oscillations.     

关于弹性应力波的三种传播模式

分析了小变形情况下变形体的平动变形和转动变形,利用连续介质的动量和动量矩守恒方程,应用各向同性线弹性体的本构关系和偶应力本构关系,提出无限弹性介质中存在体积波(压力波)、旋转波(偶应力波)和偏斜波(偏斜应力波).旋转波和偏斜波均满足形式一致的四阶波动方程,但引起不同的运动学行为和应力状态,四阶旋转波和偏斜波的传播速度不再是依赖材料参数的常值.不计旋转变形时,各向同性弹性固体中只有体积波和二阶偏斜波的传播,这时传播速度均为常数.在3种波动模式中,体积波与传统弹性应力波理论完全一致,四阶偏斜波可退化为二阶偏斜波,但后者不同于传统应力波理论中以位移作为波函数的二阶剪切波.从变形运动学与内力的关系以及能量传播的角度分析了传统应力波理论中关于二阶旋转波和二阶剪切波存在的问题.     

The effect of anisotropic heat transport in the earth's core on the geodynamo

Intermediate dynamos are axisymmetric, spherical models that evade Cowling's theorem by invoking an α-effect to create the meridional magnetic field from the zonal. Usually the energy source maintaining the motions is a specified thermal wind, but here the dynamo is driven by the buoyancy created by a uniform distribution of heat sources. It has been argued by Braginsky and Meytlis (this journal, vol. 55, 1990) that, in a rapidly rotating, strongly magnetic system such as the Earth's core, heat is transported principally by a small-scale turbulence that is highly anisotropic. They conclude that the diffusion of heat parallel to the rotation axis is then significantly greater than it is in directions away from that axis. A preliminary study of the consequences of this idea is reported here. Solutions are derived numerically using both isotropic and non-isotropic thermal diffusivity tensors, and the results are compared. It is shown that even a small degree of anisotropy can materially alter the character of the dynamo.     

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.     

Behavior of the geodynamo during reversal: A phenomenological model

The solar isotopic composition of Sm is decomposed into s, r andp components. The anomaly pattern discovered [1] in EK1-04 Allende inclusion can be presented as a fractionation of the average s-pattern from the average r-pattern. This representation requires a fractionation of 0.029% (amu)^?1 and either (1) a 0.42% deficiency of s relative to r and a 0.15% deficiency of p relative to r, or (2) a 0.42% excess of r relative to s and a 0.27% excess of p relative to s. The nature of this anomaly suggests a systematic physical fractionation of r, s and p nuclei from each other in the initial condition leading to EK1-04. A neighboring supernova injection would not be expected to produce this anomaly.     

Intermittence and peculiarities of a statistic characteristic of the geomagnetic field in geodynamo models

The analysis of the statistical characteristics of the geomagnetic field generated in the numerical geodynamo models has shown that the distribution of the spherical harmonic coefficients in some cases is not Gaussian but, instead, has much in common with the Laplace distribution. The shape of the corresponding histograms depends on the time scale, which allows interpreting the obtained data in terms of a mixture of Gaussian distributions. The similar effects associated with the intermittence were observed in the experiments in a turbulent fluid flow. Hence, the behavior of secular variations in the magnetic field of the Earth should perhaps be described in terms of a mixture of several Gaussian stationary processes corresponding to switching between the different regimes of geodynamo generation.     

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.     

Secular variation in numerical geodynamo models with lateral variations of boundary heat flow

We study magnetic field variations in numerical models of the geodynamo, with convection driven by nonuniform heat flow imposed at the outer boundary. We concentrate on cases with a boundary heat flow pattern derived from seismic anomalies in the lower mantle. At a Rayleigh number of about 100 times critical with respect to the onset of convection, the magnetic field is dominated by the axial dipole component and has a similar spectral distribution as Earth’s historical magnetic field on the core-mantle boundary (CMB). The time scales of variation of the low-order Gauss coefficients in the model agree within a factor of two with observed values. We have determined the averaging time interval needed to delineate deviations from the axial dipole field caused by the boundary heterogeneity. An average over 2000 years (the archeomagnetic time scale) is barely sufficient to reveal the long-term nondipole field. The model shows reduced scatter in virtual geomagnetic pole positions (VGPs) in the central Pacific, consistent with the weak secular variation observed in the historical field. Longitudinal drift of magnetic field structures is episodic and differs between regions. Westward magnetic drift is most pronounced beneath the Atlantic in our model. Although frozen flux advection by the large-scale flow is generally insufficient to explain the magnetic drift rates, there are some exceptions. In particular, equatorial flux spot pairs produced by expulsion of toroidal magnetic field are rapidly advected westward in localized equatorial jets which we interpret as thermal winds.     

Three distinct regimes of volcanic tremor associated with the eruption of Shishaldin Volcano, Alaska 1999

Tremor signals associated with the eruption of Shishaldin Volcano on 19 and 23 April 1999 were the strongest recorded anywhere in the Aleutian Arc by the Alaska Volcano Observatory (AVO) in its 10-year history. Reduced displacements (D_R) reached 23 cm² on 19 April and 43 cm² on 23 April. During the activity, D_R and spectral data with a frequency resolution of 0.1 Hz were computed and put on the World Wide Web every 10 min. These data are analyzed here. The general temporal patterns of seismicity of these eruption events were similar, but the eruptions and their effects quite different. The 19 April event is known to have culminated in a sub-Plinian phase, which ejected ash to an altitude of 16 km. Despite higher amplitudes and the largest hotspot from satellite data, the 23 April event produced little ash reaching only 6 km altitude. For several hours prior to the sub-Plinian phase on 19 April, tremor with a peak frequency of 1.3 Hz intensified. During the sub-Plinian phase the peak frequency increased to 4-8 Hz. However, in 15 h after the eruption, three episodes of stronger tremor occurred with a lower 1.0-Hz peak, alternating with weaker tremor with a 1.3-Hz peak. These transitions correspond to D_R=~8 cm². Although these strong tremor episodes produced higher D_R levels than the sub-Plinian phase, data from a pressure sensor show that only strong Strombolian explosions occurred. The suite of observations suggests three distinct tremor regimes that may correspond to slug flow, bubbly flow, and sustained strong eruptions, or a cyclic change in source parameters (e.g., geometry, sound speed, or ascent rate). This behavior occurred at Shishaldin only during the April 1999 sequence, and we are not aware of similar behavior at other volcanoes.     

Secondary airflow and sediment transport in the lee of a reversing dune

Lee-side windspeed and sediment transport were measured over a small (1·2 m) transverse ridge in the Silver Peak dunefield, west-central Nevada, USA, using an intensive array of 25 cup anemometers and seven total flux traps. During crest-transverse and transporting flow conditions (u_0·3crest ≈ 8·4 m s⁻¹), windspeed near the surface of the lee slope averaged half (48 per cent) that of crest speeds. Dimensionless speeds in the separation zone ranged from 0·2 to 0·8 that of the outer flow (u₁₂). Along the boundary of the separation cell, windspeed increased by 10 per cent of the crest speed before separation. Equilibrium of upper and lower wake regions was not observed by the documented eight dune heights, suggesting that wake recovery may not occur over closely spaced dunes. Sediment transport measured directly on both the lee slope and interdune surfaces averaged approximately 15 per cent of crest inputs. This suggests that a significant amount (c. 70–95 per cent) of sediment transported over the crest moved as fallout. For this data set, flux was approximately proportional to the cube of the near-surface windspeed (u_0·3) and in general there was an order of magnitude difference between flux measured at the crest and that measured within the separation zone. Transport direction in the separation zone was acutely oblique to the incident direction owing to secondary flow deflection. Beyond the interdune, transport direction progressed from oblique to crest-transverse. This indicates that an appreciable amount of sediment may move laterally along the lee slope and interdune corridor under crest-transverse flows. Regarding the grain size and sorting properties of transported sediment, there was no significant difference in mean grain size over the dune, although in general particles were finer and more poorly sorted in the lee. Copyright © 1999 John Wiley & Sons, Ltd.     

Tides and mixing in the northwestern East China Sea Part I: Rotating and reversing tidal flows

Bottom-mounted ADV and ADCP instruments in combination with CTD profiling measurements taken along the Chinese coast of the East China Sea were used to study the vertical structure of temperature, salinity, and velocity in reversing tidal currents on a shallow inner shelf and in rotating tidal flows over a deeper sloping bottom of the outer shelf. These two regimes of barotropic tide affect small-scale dynamics in the lower part of the water column differently. The reversing flow was superimposed by seiches of ∼2.3 h period generated in semienclosed Jiaozhou Bay located nearby. As the tidal vector rotates over the sloping bottom, the height of the near-bottom logarithmic layer is subjected to tidal-induced variations. A maximum of horizontal velocity U_max appears at the upper boundary of the log layer during the first half of the current vector rotation from the minor to the major axis of tidal ellipse. In rotating tidal flow, vertical shear generated at the seafloor, propagated slowly to the water interior up to the height of U_max, with a phase speed of ∼5 m/h. The time-shifted shear inside the water column, relative to the shear at the bottom, was associated with periodically changing increases and decreases of the tidal velocity above the log layer toward the sea surface. In reversing flows, the shear generated near the bottom and the shear at the upper levels were almost in phase.