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1.
Ján Boďa 《Studia Geophysica et Geodaetica》1992,36(2):139-150
Summary Our discussion is concerned with the common effect of the non-uniformity of layer rotation and stratification. We have assumed a model of differential rotation with the upper part of the layer rotating more slowly, the bottom part more quickly. The upper part of the layer is stratified stably, the bottom part unstably.The thermal instabilities are preferred in the strong differential rotation case and they are the most easily excited by a strong magnetic field (102–103). The direction of its propagation is westward in the uniformly stratified layer and eastward in the non-uniformly stratified layer. 相似文献
2.
Linear magnetoconvection in a model of a non-uniformly stratified horizontal rotating fluid layer with a toroidal magnetic
field is investigated for no-slip and finitely electrically conductive boundaries and with very thin stably stratified upper
sublayer. The basic parabolic temperature profile is determined by the temperature difference between the boundaries and by
the homogeneous heat source distribution in the layer. This results in a density pattern, in which a stably stratified upper
sublayer is present. The developed diffusive perturbations (modes) are strongly affected by the complicated coupling of viscous,
thermal and magnetic diffusive processes. The calculations were performed for various values of Roberts number (q ≪ 1 and
q = O(1)). The mean electromotive force produced by the developed hydromagnetic instabilities is investigated to find the modes,
which can be appropriate for creating the α-effect. It was found that the azimuthal part of the EMF is dominant for westward
modes when the Elsasser number Λ ≲ O(1). 相似文献
3.
Abstract Results are presented of a numerical study of marginal convection of electrically conducting fluid, permeated by a strong azimuthal magnetic field, contained in a circular cylinder rotating rapidly about its vertical axis of symmetry. To this basic state is added a geostrophic flow UG (s), constant on geostrophic cylinders radius s. Its magnitude is fixed by requiring that the Lorentz forces induced by the convecting mode satisfy Taylor's condition. The nonlinear mathematical problem describing the system was developed in an earlier paper (Skinner and Soward, 1988) and the predictions made there are confirmed here. In particular, for small values of the Roberts number q which measures the ratio of the thermal to magnetic diffusivities, two distinct regions can be recognised within the fluid with the outer region moving rapidly compared to the inner. Otherwise, conditions for the onset of instability via the Taylor state (UG 0) do not differ significantly from those appropriate to the static (UG = 0) basic state. The possible disruption of the Taylor states by shear flow instabilities is discussed briefly. 相似文献
4.
Abstract This paper develops further a convection model that has been studied several times previously as a very crude idealization of planetary core dynamics. A plane layer of electrically-conducting fluid rotates about the vertical in the presence of a magnetic field. Such a field can be created spontaneously, as in the Childress—Soward dynamo, but here it is uniform, horizontal and externally-applied. The Prandtl number of the fluid is large, but the Ekman, Elsasser and Rayleigh numbers are of order unity, as is the ratio of thermal to magnetic diffusivity. Attention is focused on the onset of convection as the temperature difference applied across the layer is increased, and on the preferred mode, i.e., the planform and time-dependence of small amplitude convection. The case of main interest is the layer confined between electrically-insulating no-slip walls, but the analysis is guided by a parallel study based on illustrative boundary conditions that are mathematically simpler. 相似文献
5.
The linear magnetoconvection in the rotating uniformly as well as non-uniformly stratified horizontal layer with azimuthal magnetic field is investigated for the various mechanical and electrical boundary conditions and especially, for various values of Roberts number. The developed diffusive perturbations (modes) are strongly influenced not only by the mentioned properties of boundaries but also by complicated coupling of viscous, thermal and magnetic diffusive processes. The mean electromotive force produced by developed hydromagnetic instabilities is also investigated to determine the hydromagnetic processes which are appropriate for -effect. The presented paper is an unification of hitherto published results of the authors and gives a short survey of many developments of corresponding model by Soward (1979). 相似文献
6.
D. R. Fearn 《地球物理与天体物理流体动力学》2013,107(1):103-126
Abstract A linear analysis is used to study the stability of a rapidly rotating, electrically-conducting, self-gravitating fluid sphere of radius r 0, containing a uniform distribution of heat sources and under the influence of an azimuthal magnetic field whose strength is proportional to the distance from the rotation axis. The Lorentz force is of a magnitude comparable with that of the Coriolis force and so convective motions are fully three-dimensional, filling the entire sphere. We are primarily interested in the limit where the ratio q of the thermal diffusivity κ to the magnetic diffusivity η is much smaller than unity since this is possibly of the greatest geophysical relevance. Thermal convection sets in when the temperature gradient exceeds some critical value as measured by the modified Rayleigh number Rc. The critical temperature gradient is smallest (Rc reaches a minimum) when the magnetic field strength parameter Λ ? 1. [Rc and Λ are defined in (2.3).] The instability takes the form of a very slow wave with frequency of order κ/r 2 0 and its direction of propagation changes from eastward to westward as Λ increases through Λ c ? 4. When the fluid is sufficiently stably stratified and when Λ > Λm ? 22 a new mode of instability sets in. It is magnetically driven but requires some stratification before the energy stored in the magnetic field can be released. The instability takes the form of an eastward propagating wave with azimuthal wavenumber m = 1. 相似文献
7.
本文研究了双扩散效应对处于地球物理极限q→0条件下旋转分层导电流体的磁流体动力学（MHD）不稳定性的影响。研究发现,只要|RS|足够大,对流总能在流体静力稳定分层的导电流体中发展。当磁场作用较弱,即Λ～Ο（1）时,对所有可能的角向波数m优先发展的是双扩散不稳定性。当Rs>0时,流体中发生几乎不变的“指状”对流。当Rs<0时,流体中发生缓慢东向运行的“扩散”振荡。当磁场作用较强,即Λ≥ΛM时,与原始Soward模式类似,优先发展的仅是m=1磁力驱动不稳定性,并东向运行,但双扩散效应使得正RT不稳定性与负RT不稳定性间的对称性破缺。 相似文献
8.
Abstract The weak-field Benard-type dynamo treated by Soward is considered here at higher levels of the induced magnetic field. Two sources of instability are found to occur in the intermediate field regime M ～ T 1/12, where M and T are the Hartmann and Taylor numbers. On the time scale of magnetic diffusion, solutions may blow up in finite time owing to destabilization of the convection by the magnetic field. On a faster time scale a dynamic instability related to MAC-wave instability can also occur. It is therefore concluded that the asymptotic structure of this dynamo is unstable to virtual increases in the magnetic field energy. In an attempt to model stabilization of the dynamo in a strong-field regime we consider two approximations. In the first, a truncated expansion in three-dimensional plane waves is studied numerically. A second approach utilizes an ad hoc set of ordinary differential equations which contains many of the features of convection dynamos at all field energies. Both of these models exhibit temporal intermittency of the dynamo effect. 相似文献
9.
A.M. Soward 《Physics of the Earth and Planetary Interiors》1979,20(2-4):134-151
Various models of thermal convection in rapidly rotating fluids permeated by strong magnetic fields are discussed. Particular attention is paid to the possibility that the magnetic field can be maintained by dynamo action rather than by externally applied electric currents. Two dynamo models are given particular attention. They are the plane layer model of Childress and Soward (1972) and the annulus model of Busse (1975). Though these models do not totally resolve the geodynamo problem, they do highlight important features of hydromagnetic dynamos. As a result some speculations are made about the true character of the geodynamo. 相似文献
10.
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 Y 2² 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. 相似文献
11.
The presence of outer stably stratified layers in planetary cores has been suggested for Earth, Saturn and Mercury. In this study, we use a 3-D numerical dynamo model to investigate the effects of a thin stable layer surrounding a convecting interior on the produced magnetic field. We find that a stable layer can destabilize the field morphology through a thermal wind that produces unfavorable zonal flows throughout the core. The direction of these zonal flows is prograde in equatorial regions, unlike a model with no stable layer that has retrograde equatorial flows. Our models therefore suggest that the Earth does not have a stable layer since we observe a westward drift as opposed to an eastward drift. For Saturn, we find that due to coupling of the flows in the stable and unstable layers, the layer does not act to shear out the non-axisymmetry in the observed magnetic field, and therefore cannot explain Saturn’s axisymmetric magnetic field. For Mercury, we find that if the stable layer is thin, it can actively produce strong or weak surface fields and not necessarily attenuate smaller scale features through the skin effect. 相似文献
12.
Ajay Manglik Johannes Wicht Ulrich R. Christensen 《Earth and Planetary Science Letters》2010,289(3-4):619-628
A recent dynamo model for Mercury assumes that the upper part of the planet's fluid core is thermally stably stratified because the temperature gradient at the core–mantle boundary is subadiabatic. Vigorous convection driven by a superadiabatic temperature gradient at the boundary of a growing solid inner core and by the associated release of light constituents takes place in a deep sub-layer and powers a dynamo. These models have been successful at explaining the observed weak global magnetic field at Mercury's surface. They have been based on the concept of codensity, which combines thermal and compositional sources of buoyancy into a single variable by assuming the same diffusivity for both components. Actual diffusivities in planetary cores differ by a large factor. To overcome the limitation of the codensity model, we solve two separate transport equations with different diffusivities in a double diffusive dynamo model for Mercury. When temperature and composition contribute comparable amounts to the buoyancy force, we find significant differences to the codensity model. In the double diffusive case convection penetrates the upper layer with a net stable density stratification in the form of finger convection. Compared to the codensity model, this enhances the poloidal magnetic field in the nominally stable layer and outside the core, where it becomes too strong compared to observation. Intense azimuthal flow in the stable layer generates a strong axisymmetric toroidal field. We find in double diffusive models a surface magnetic field of the observed strength when compositional buoyancy plays an inferior role for driving the dynamo, which is the case when the sulphur concentration in Mercury's core is only a fraction of a percent. 相似文献
13.
In Kim et al. (Kim, E., Hughes, D.W. and Soward, A.M., “An investigation into high conductivity dynamo action driven by rotating convection”, Geophys. Astrophys. Fluid Dynam. 91, 303–332 ().) we investigated kinematic dynamo action driven by rapidly rotating convection in a cylindrical annulus. Here we extend this work to consider self-consistent nonlinear dynamo action in which the back-reaction of the Lorentz force on the flow is taken into account. In particular, we investigate, as a function of magnetic Prandtl number, the evolution of an initially weak magnetic field in two different types of convective flow – one chaotic and the other integrable. On saturation, the latter shows a systematic dependence on the magnetic Prandtl number whereas the former appears not to. In addition, we show how, in keeping with the findings of Cattaneo et al. (Cattaneo, F., Hughes, D.W. and Kim, E., “Suppression of chaos in a simplified nonlinear dynamo model”, Phys. Rev. Lett. 76, 2057–2060 ().), saturation of the growth of the magnetic field is brought about, for the originally chaotic flow, by a strong suppression of chaos. 相似文献
14.
Marginal instabilities in a horizontal unstably stratified rapidly rotating fluid layer permeated by an azimuthal magnetic field growing linearly with distance from the vertical rotation axis, are investigated in dependence on electromagnetic boundary conditions and Roberts number
. Electrical conductivities of perfectly thermally conducting boundaries are either infinite or finite Earthlike ones.
Following Soward's (1979) results the case of
gives the instabilities of MAC-waves with much greater frequencies than for the case of q 1. Critical frequencies of MAC waves are most sensitive on Roberts number for q 1 and lose this sensitivity for q2. On the other hand the critical Rayleigh numbers are slightly dependent on q 1. Many qualitative differences in the dependences on q do exist for infinitely and finitely conducting boundaries. The former do not allow fast eastward modes for q 1 and the latter, e.g. allow eastward MC-waves with azimuthal wave number m = 1. The MC-waves are almost independent on Roberts number q. 相似文献
15.
ABSTRACTThe present study aims to link the dynamics of geophysical fluid flows with their vortical structures in physical space and to study the transition of these structures due to the control parameters. The simulations are carried in a rectangular box filled with liquid gallium for three different cases, namely, Rayleigh–Bénard convection (RBC), magnetoconvection (MC) and rotating magnetoconvection (RMC). The physical setup and material properties are similar to those considered by Aurnou and Olson in their experimental work. The simulated results are validated with theoretical results of Chandrasekhar and experimental results of Aurnou and Olson. The results are also topologically verified with the help of Euler number given by Ma and Wang. For RBC, the onset is obtained at Ra greater than 1708 and at this Ra, the symmetric rolls are orientated in/along a horizontal axis. As the value of Ra increases further, the width of the horizontal rolls starts to amplify. It is observed that these two-dimensional rolls are nothing but the cross-sections of three-dimensional (3D) cylindrical rolls with wave structures. When the vertically imposed magnetic field is added to RBC, the onset of convection is delayed due to the effect of Lorentz force on the thermal buoyancy force. The presence of 3D rectangular structures is highlighted and analysed. When the magnetically influenced rectangular box rotates about vertical axis at low rotation rates in magnetoconvection model, the onset of convection gets further delayed by magnetic field, which is in general agreement with the theoretical predictions. The critical Ra increases linearly with magnetic field intensity. Coherent thermal oscillations are detected near the onset of convection, at moderate rotation rates. 相似文献
16.
Michael I. Bergman 《地球物理与天体物理流体动力学》2013,107(1-4):151-176
Abstract The stratification profile of the Earth's magnetofluid outer core is unknown, but there have been suggestions that its upper part may be stably stratified. Braginsky (1984) suggested that the magnetic analog of Rossby (planetary) waves in this stable layer (the ‘H’ layer) may be responsible for a portion of the short-period secular variation. In this study, we adopt a thin shell model to examine the dynamics of the H layer. The stable stratification justifies the thin-layer approximations, which greatly simplify the analysis. The governing equations are then the Laplace's tidal equations modified by the Lorentz force terms, and the magnetic induction equation. We linearize the Lorentz force in the Laplace's tidal equations and the advection term in the magnetic induction equation, assuming a zeroth order dipole field as representative of the magnetic field near the insulating core-mantle boundary. An analytical β-plane solution shows that a magnetic field can release the equatorial trapping that non-magnetic Rossby waves exhibit. A numerical solution to the full spherical equations confirms that a sufficiently strong magnetic field can break the equatorial waveguide. Both solutions are highly dissipative, which is a consequence of our necessary neglect of the induction term in comparison with the advection and diffusion terms in the magnetic induction equation in the thin-layer limit. However, were one to relax the thin-layer approximations and allow a radial dependence of the solutions, one would find magnetic Rossby waves less damped (through the inclusion of the induction term). For the magnetic field strength appropriate for the H layer, the real parts of the eigenfrequencies do not change appreciably from their non-magnetic values. We estimate a phase velocity of the lowest modes that is rather rapid compared with the core fluid speed typically presumed from the secular variation. 相似文献
17.
18.
M. R. E. Proctor 《地球物理与天体物理流体动力学》2013,107(1):127-145
Abstract A magnetohydrodynamic, dynamo driven by convection in a rotating spherical shell is supposed to have averages that are independent of time. Two cases are considered, one driven by a fixed temperature difference R and the other by a given internal heating rate Q. It is found that when q, the ratio of thermal conductivity to magnetic diffusivity, is small, R must be of order q ?4/3 and Q of order q ?2 for dynamo action to be possible; q is small in the Earth's core, so it is hoped that the criteria will prove useful in practical as well as theoretical studies of dynamic dynamos. The criteria can be further strengthened when the ohmic dissipation of the field is significant in the energy balance. The development includes the derivation of two necessary conditions for dynamo action, both based on the viscous dissipation rate of the velocity field that drives the dynamo. 相似文献
19.
20.
D. J. Stevenson 《地球物理与天体物理流体动力学》2013,107(1-2):113-127
Abstract If a conducting fluid shell is undergoing spin-axisymmetric differential rotation and overlies the dynamo generating region of a planet then it is capable of greatly reducing the non-spin-axisymmetric components of the generated field, provided the appropriate magnetic Reynolds number is large. The model, closely related to the electromagnetic skin effect, is quantified and applied to Saturn. The observed small dipole tilt (～ 1°) of Saturn's magnetic field can be explained because of the presence of a stably stratified conducting layer overlying the dynamo region. This layer is a predicted consequence of the thermal evolution, arises because of the limited solubility of helium in metallic hydrogen (Stevenson, 1980), and appears to be required by the Voyager infrared observations indicating depletion of helium from Saturn's atmosphere. The much larger dipole tilt angles of Jupiter and the Earth indicate the absence of any such stable, differentially rotating layer with a large magnetic Reynolds number. 相似文献