共查询到20条相似文献，搜索用时 31 毫秒
1.
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. 相似文献
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Chao-Ho Sung 《地球物理与天体物理流体动力学》2013,107(1):179-182
Abstract Sufficient conditions for stability are established for the magnetic field problem of the Earth's core considered by Braginsky. 相似文献
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Yu. A. Brodsky 《地球物理与天体物理流体动力学》2013,107(3-4):281-304
Abstract Perturbation theory methods are developed for the kinematic geodynamo equations. The vector Green's function is constructed for the unperturbed equation, which includes the axisymmetric differential rotation. While investigating the perturbation series, we consider a special case in which the decay rates of the axisymmetric toroidal and poloidal dipoles are degenerate. For a number of models within the framework of the theory developed, estimates are given for generation conditions and for observed characteristics of the geomagnetic field. 相似文献
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Abstract Starting from Euler's equations of motion a nonlinear model for internal waves in fluids is developed by an appropriate scaling and a vertical integration over two layers of different but constant density. The model allows the barotropic and the first baroclinic mode to be calculated. In addition to the nonlinear advective terms dispersion and Coriolis force due to the Earth's rotation are taken into account. The model equations are solved numerically by an implicit finite difference scheme. In this paper we discuss the results for ideal basins: the effects of nonlinear terms, dispersion and Coriolis force, the mechanism of wind forcing, the evolution of Kelvin waves and the corresponding transport of particles and, finally, wave propagation over variable topography. First applications to Lake Constance are shown, but a detailed analysis is deferred to a second paper [Bauer et al. (1994)]. 相似文献
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Susan Friedlander 《地球物理与天体物理流体动力学》2013,107(1-2):151-167
Abstract The effects of compressibility on the stability of internal oscillations in the Earth's fluid core are examined in the context of the subseismic approximation for the equations of motion describing a rotating, stratified, self-gravitating, compressible fluid in a thick shell. It is shown that in the case of a bounded fluid the results are closely analogous to those derived under the Boussinesq approximation. 相似文献
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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. 相似文献
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A multi-layered kinematic dynamo model: implications of a stratified upper layer in the Earth's core
It has been suggested that there exists a stably stratified electrically conducting layer at the top of the Earth's outer fluid core and that lateral temperature gradients in the lower mantle is capable of a driving thermal-wind-type flow near the core–mantle boundary. We investigate how such a flow in a stable layer could influence the geomagnetic field and the geodynamo using a very simple two-dimensional kinematic dynamo model in Cartesian geometry. The dynamo has four layers representing the inner core, convecting lower outer core, stable upper core, and insulating mantle. An α2 dynamo operates in the convecting outer core and a horizontal shear flow is imposed in the stable layer. Exact dynamo solutions are obtained for a range of parameters, including different conductivities for the stable layer and inner core. This allows us to connect our solutions with known, simpler solutions of a single-layer α2 dynamo, and thereby assess the effects of the extra layers. We confirm earlier results that a stable, static layer can enhance dynamo action. We find that shear flows produce dynamo wave solutions with a different spatial structure from the steady α2 dynamos solutions. The stable layer controls the behavior of the dynamo system through the interface conditions, providing a new means whereby lateral variations on the boundary can influence the geomagnetic field. 相似文献
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Paul H. Roberts 《地球物理与天体物理流体动力学》2013,107(1-4):3-31
Abstract This is an attempt to predict the next fifteen years of geodynamo theory, and to assess the success potential of current directions of research. A new phenomenon, the subcriticality of a model-Z geodynamo, is described. 相似文献
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S. D. London 《地球物理与天体物理流体动力学》2013,107(3-4):251-268
Abstract Numerical work indicates that resistive instability may be the dominant mode of instability in the Earth's outer core for realistic core parameter regimes. In this paper, we assume that the Elsasser number is large in order to obtain an asymptotic analysis of resistive instability in an electrically conducting fluid confined to a rotating cylindrical shell of infinite extent in the axial direction. The dimensionless equations of motion are linearized about an ambient magnetic field which is purely azimuthal and depends only on the cylindrical radial variable. Applying the theory of ordinary differential equations with a large parameter, we obtain an asymptotic approximation to the solution. Relatively simple analytic expressions for the complex frequencies are obtained by applying the boundary conditions for insulating boundaries at the cylindrical sidewalls and then assuming that the ambient magnetic field vanishes at one or both of those sidewalls. The results appear to be consistent with previous numerical work. 相似文献
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Martin Schrinner Karl-Heinz Rädler Matthias Rheinhardt Ulrich R. Christensen 《地球物理与天体物理流体动力学》2013,107(2):81-116
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. 相似文献
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Alexander M. krigel 《地球物理与天体物理流体动力学》2013,107(3):213-223
Abstract Friedmann's equation and the potential vorticity equation are generalised for turbulent motion. The generalised equations incorporate some new phenomena connected with turbulent transport of mass. It is proved that, if ?×[S×Ω+S(?·S)]≠0 where Ω is the absolute vorticity of the velocity and S is the turbulent density flux, then the Helmholtz-Kelvin theorem concerning the conservation of the velocity circulation around a closed path is violated and the potential vorticity is not a Lagrangian adiabatic invariant. The effects of this turbulent transport of mass on the creation or dissipation of vorticity discussed here is not equivalent to effects of baroclinicity or viscosity. Some possible implications of the new circulation theorem in geophysical and astrophysical fluid dynamics are discussed. 相似文献
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ABSTRACTTurbulence in the Earth's outer core not only increases all diffusive coefficients, but it can lead to their anisotropic properties. Therefore, the model of rotating magnetoconvection in horizontal plane layer rotating about vertical axis and permeated by homogeneous horizontal magnetic field, influenced by anisotropic diffusivities, viscosity and thermal diffusivity, is advanced by considering the magnetic diffusivity as anisotropic too. The case of full anisotropy, i.e. all coefficients anisotropic, is compared with both the case possessing isotropic diffusion coefficients and the case of partial anisotropy, i.e. mixed case with isotropic and anisotropic diffusive coefficients (viscosity and thermal diffusivity anisotropic and magnetic diffusivity isotropic). The existence and preference of instabilities is sensitive to all non-dimensional parameters, as well as on anisotropic parameter, the ratio of horizontal and vertical diffusivities. Two types of anisotropy, BM (introduced by Braginsky and Meytlis) and SA (stratification anisotropy) are studied. BM as well as SA were applied by ?oltis and Brestenský to the study of the partial anisotropy; this study is extended, in this paper, to full anisotropy cases (full SA and full BM) and it is shown that the style of convection given by the onset of stationary modes is more affected by anisotropic diffusivities in BM than in SA anisotropy. The important influence of strong anisotropies in the Earth's core dynamics is stressed. 相似文献
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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. 相似文献
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S. L. Shalimov 《Izvestiya Physics of the Solid Earth》2006,42(6):460-466
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. 相似文献
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Willem V. R. Malkus 《地球物理与天体物理流体动力学》2013,107(1):267-278
AbstractHiggins and Kennedy (1971) concluded that the Earth's fluid core has a stable stratification if it is at its melting point. Busse (1972) and Elsasser suggested as an alternative that a hydrostatic-isentropic distribution of particulate solid can produce neutral stability in a partially molten core. Here this suggestion is quantified and a determination is made of the efficiency of the production of fluid motion from the heat flux. This is used to establish that macroscopic convection can exist only if the particulate solid is of sufficiently small size. A thermal history of the core compatible with upper mantle heat flux is advanced in which it is suggested that the inner core is a fairly recent feature. The implication of these results for convection-driven and precession-driven dynamos is that both can function for a small enough suspended particulate, that the convection-dynamo will fail for particles greater than one micron in diameter, and that the precession-driven dynamo probably cannot survive particles greater than ten microns in diameter. 相似文献
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Masaki Matsushima 《地球物理与天体物理流体动力学》2013,107(6):630-642
A thermal diffusive process in the Earth's core is principally enhanced by small-scale flows that are highly anisotropic because of the Earth's rapid rotation and a strong magnetic field. This means that a thermal eddy diffusivity should not be a scalar but a tensor. The effect of such anisotropic tensor diffusivity, which is to be prescribed, on dynamics in the Earth's core is investigated through numerical simulations of magnetoconvection in a rapidly rotating system. A certain degree of anisotropy has an insignificant effect on the character, like kinetic and magnetic energies, of magnetoconvection in a small region with periodic boundaries in the three directions. However, in a region with top and bottom rigid boundary surfaces, kinetic and magnetic energies of magnetoconvection can be altered by the same degree of anisotropy. This implies that anisotropic tensor diffusivity affects on dynamics in the core, in particular near the boundary surfaces. 相似文献
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《Earth and Planetary Science Letters》2007,253(1-2):172-195
The Earth's magnetic field changed its polarity from the last reversed into today's normal state approximately 780 000 years ago. While before and after this so called Matuyama/Brunhes reversal, the Earth magnetic field was essentially an axial dipole, the details of its transitional structure are still largely unknown. Here, a Bayesian inversion method is developed to reconstruct the spherical harmonic expansion of this transitional field from paleomagnetic data. This is achieved by minimizing the total variational power at the core–mantle boundary during the transition under paleomagnetic constraints. The validity of the inversion technique is proved in two ways. First by inverting synthetic data sets from a modeled reversal. Here it is possible to reliably reconstruct the Gauss coefficients even from noisy records. Second by iteratively combining four geographically distributed high quality paleomagnetic records of the Matuyama/Brunhes reversal into a single geometric reversal scenario without assuming an a priori common age model. The obtained spatio-temporal reversal scenario successfully predicts most independent Matuyama/Brunhes transitional records. Therefore, the obtained global reconstruction based on paleomagnetic data invites to compare the inferred transitional field structure with results from numerical geodynamo models regarding the morphology of the transitional field. It is found that radial magnetic flux patches form at the equator and move polewards during the transition. Our model indicates an increase of non-dipolar energy prior to the last reversal and a non-dipolar dominance during the transition. Thus, the character and information of surface geomagnetic field records is strongly site dependent. The reconstruction also offers new answers to the question of existence of preferred longitudinal bands during the transition and to the problem of reversal duration. Different types of directional variations of the surface geomagnetic field, continuous or abrupt, are found during the transition. Two preferred longitudinal bands along the Americas and East Asia are not predicted for uniformly distributed sampling locations on the globe. Similar to geodynamo models with CMB heatflux derived from present day lower mantle heterogeneities, a preference of transitional VGPs for the Pacific hemisphere is found. The paleomagnetic duration of reversals shows not only a latitudinal, but also a longitudinal variation. Even the paleomagnetically determined age of the reversal varies significantly between different sites on the globe. The described Bayesian inversion technique can easily be applied to other high quality full vector reversal records. Also its extension to inversion of secular variation and excursion data is straightforward. 相似文献