共查询到20条相似文献，搜索用时 31 毫秒
1.
2.
3.
4.
5.
Abstract It is demonstrated that the steady tangential velocity vs at the closed surface δK of a perfect fluid conductor bounded by a rigid, impenetrable exterior can be uniquely determined from knowledge of the normal component of the time varying magnetic flux density B n, on δK. In the context of a simple earth model consisting of an electrically insulating mantle surrounding a perfectly conducting core, the assumption of steady flow provides enough extra information to eliminate the toroidal ambiguity in B nv and to allow derivation of a unique, global flow at the top of the core from a model of the geomagnetic field. 相似文献
6.
Abstract We study the nonlinear asymptotic thin disc approximation to the mean field dynamo equations, as applicable to spiral galaxies. The circumstances in which sharp magnetic field structures (fronts) can propagate radially are investigated, and an expression for the speed of propagation derived. We find that the speed of an interior front is proportional to η//R ? (where η is the diffusivity and Rt the galactic radius), whereas an exterior front moves with speed of order , where γ is the local growth rate of the dynamo. Numerical simulations are presented, that agree well with our asymptotic results. Further, we perform numerical experiments using the 'no-z' approximation for thin disc dynamos, and show that the propagation of magnetic fronts in this approximation can also be understood in terms of our asymptotic results. 相似文献
7.
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
8.
A key non-linear mechanism in a strong-field geodynamo is that a finite amplitude magnetic field drives a flow through the Lorentz force in the momentum equation and this flow feeds back on the field-generation process in the magnetic induction equation, equilibrating the field. We make use of a simpler non-linear?α?2-dynamo to investigate this mechanism in a rapidly rotating fluid spherical shell. Neglecting inertia, we use a pseudo-spectral time-stepping procedure to solve the induction equation and the momentum equation with no-slip velocity boundary conditions for a finitely conducting inner core and an insulating mantle. We present calculations for Ekman numbers (E) in the range 2.5× 10?3 to 5.0× 10?5, for?α?=α 0cos?θ?sin?π?(r?ri ) (which vanishes on both inner and outer boundaries). Solutions are steady except at lower E and higher values of?α?0. Then they are periodic with a reversing field and a characteristic rapid increase then equally rapid decrease in magnetic energy. We have investigated the mechanism for this and shown the influence of Taylor's constraint. We comment on the application of our findings to numerical hydrodynamic dynamos. 相似文献
9.
David R. Fearn 《地球物理与天体物理流体动力学》2013,107(1-2):137-162
Abstract A cylindrical annulus containing a conducting fluid and rapidly rotating about its axis is a useful model for the Earth's core. With a shear flow U 0(s)∮, magnetic field B 0(s)∮, and temperature distribution T o(s) (where (s, ∮, z) are cylindrical polar coordinates), many important properties of the core can be modelled while a certain degree of mathematical simplicity is maintained. In the limit of rapid rotation and at geophysically interesting field strengths, the effects of viscous diffusion and fluid inertia are neglected. In this paper, the linear stability of the above basic state to instabilities driven by gradients of B 0 and U 0 is investigated. The global numerical results show both instabilities predicted by a local analysis due to Acheson (1972, 1973, 1984) as well as a new resistive magnetic instability. For the non-diffusive field gradient instability we looked at both monotonic fields [for which the local stability parameter Δ, defined in (1.4), is a constant] and non-monotonic fields (for which Δ is a function of s). For both cases we found excellent qualitative agreement between the numerical and local results but found the local criterion (1.6) for instability to be slightly too stringent. For the non-monotonic fields, instability is confined approximately to the region which is locally unstable. We also investigated the diffusive buoyancy catalysed instability for monotonic fields and found good quantitative agreement between the numerical results and the local condition (1.9). The new resistive instability was found for fields vanishing (or small) at the outer boundary and it is concentrated in the region of that boundary. The resistive boundary layer plays an important part in this instability so it is not of a type which could be predicted using a local stability analysis (which takes no account of the presence of boundaries). 相似文献
10.
David R. Fearn 《地球物理与天体物理流体动力学》2013,107(1-4):55-75
Abstract The first three papers in this series (Fearn, 1983b, 1984, 1985) have investigated the stability of a strong toroidal magnetic field Bo =Bo(s?)Φ [where (s?. Φ, z?) are cylindrical polars] in a rapidly rotating system. The application is to the cores of the Earth and the planets but a simpler cylindrical geometry was chosen to permit a detailed study of the instabilities present. A further simplification was the use of electrically perfectly conducting boundary conditions. Here, we replace these with the boundary conditions appropriate to an insulating container. As expected, we find the same instabilities as for a perfectly conducting container, with quantitative changes in the critical parameters but no qualitative differences except for some interesting mixing between the ideal (“field gradient”) and resistive modes for azimuthal wavenumber m=1. In addition to these modes, we have also found the “exceptional” slow mode of Roberts and Loper (1979) and we investigate the conditions required for its instability for a variety of fields Bo(s?) Roberts and Loper's analysis was restricted to the case Bo∝s? and they found instability only for m=1 and ?1 <ω<0 [where ω is the frequency non-dimensionalised on the slow timescale τx, see (1.5)]. For other fields we found the necessary conditions to be less “exceptional”. One surprising feature of this instability is the importance of inertia for its existence. We show that viscosity is an alternative destabilising agent. The standard (magnetostrophic) approximation of neglecting inertial (and viscous) terms in the equation of motion has the effect of filtering out this instability. The field strength required for this “exceptional” mode to become unstable is found to be very much larger than that thought to be present in the Earth's core, so we conclude that this mode is unlikely to play an important role in the dynamics of the core. 相似文献
11.
Johannes Wicht 《Physics of the Earth and Planetary Interiors》2002,132(4):281-302
Speculation about its possible super-rotation has drawn the attention of many geophysical researchers to the Earth’s inner core. An issue of special interest for geodynamo modelling is the influence of the inner-core conductivity. It has been suggested that the finite magnetic diffusivity of the inner core prevents more frequent reversals of the Earth’s magnetic field. We explore the possible influence of the inner-core conductivity by comparing convection-driven 3D dynamo simulations with insulating or conducting inner cores (CIC) at various parameters. The influence on the field structure in the outer core is only marginal. The time behaviour of dipole-dominated non-reversing dynamos is also little affected. Concerning reversing dynamos, the inner-core conductivity reduces the number of short dipole-polarity intervals with a typical length of a few thousand years. Reversals are always correlated with low dipole strength and these short intervals are found in periods where the dipole moment stays low. Polarity intervals longer than about 10,000 years, where the dipole moment has time recover in strength, are equally likely in insulating and CIC models. Since these latter intervals are of more geophysical relevance, we conclude that the influence of the inner-core conductivity on Earth-like reversal sequences is insignificant for the dynamo model employed here. 相似文献
12.
D. J. Ivers 《地球物理与天体物理流体动力学》2013,107(1-2):121-128
13.
Abstract In a rapidly rotating, electrically conducting fluid we investigate the thermal stability of the fluid in the presence of an imposed toroidal magnetic field and an imposed toroidal differential rotation. We choose a magnetic field profile that is stable. The familiar role of differential rotation is a stabilising one. We wish to examine the less well known destabilising effect that it can have. In a plane layer model (for which we are restricted to Roberts number q = 0) with differential rotation, U = sΩ(z)1 ?, no choice of Ω(z) led to a destabilising effect. However, in a cylindrical geometry (for which our model permits all values of q) we found that differential rotations U = sΩ(s)1 ? which include a substantial proportion of negative gradient (dΩ/ds ≤ 0) give a destabilising effect which is largest when the magnetic Reynolds number R m = O(10); the critical Rayleigh number, Ra c, is about 7% smaller at minimum than at Rm = 0 for q = 106. We also find that as q is reduced, the destabilising effect is diminished and at q = 10?6, which may be more appropriate to the Earth's core, the effect causes a dip in the critical Rayleigh number of only about 0.001%. This suggests that we see no dip in the plane layer results because of the q = 0 condition. In the above results, the Elsasser number A = 1 but the effect of differential rotation is also dependent on A. Earlier work has shown a smooth transition from thermal to differential rotation driven instability at high A [A = O(100)]. We find, at intermediate A [A = O(10)], a dip in the Rac vs. Rm curve similar to the A = 1 case. However, it has Rac ≤ 0 at its minimum and unlike the results for high A, larger values of Rm result in a restabilisation. 相似文献
14.
15.
本文以两种绝缘内核的发电机为基准,设置内核电导率与外核相同,选择了以固定速度超速旋转和在外核驱动下发生旋转的两种内核旋转模式,比较分析不同模型间的能量差异、磁场强度、磁雷诺数、磁极翻转频率和四个类地发电机参数.结果表明:对于弱偶极子发电机模型,有限导电内核的引入会对其偶极子强度的相对变化量造成较大影响,最高达103.00%;由外核驱动旋转的有限导电内核模型对于本文其他目标研究量所带来的影响比较小,均小于5%;而固定旋转速度的有限导电内核的模型对磁极翻转频率、赤道对称性和纬向性均存在较明显影响,最大变化量达124.62%.综合本文所选用的发电机模型的特征和数值分析结果,可以发现虽然由外核驱动旋转的有限导电内核模型其转速不可控且存在较大波动,但各物理量变化量与实际内核与外核的能量比更为接近,因此可以推断其驱动机制较自驱动模式更为合理可靠. 相似文献
16.
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
17.
Abstract We investigate the influence of differential rotation on magnetic instabilities for an electrically conducting fluid in the presence of a toroidal basic state of magnetic field B 0 = BMB0(r, θ)1 φ and flow U0 = UMU0 (r, θ)1φ, [(r, θ, φ) are spherical polar coordinates]. The fluid is confined in a rapidly rotating, electrically insulating, rigid spherical container. In the first instance the influence of differential rotation on established magnetic instabilities is studied. These can belong to either the ideal or the resistive class, both of which have been the subject of extensive research in parts I and II of this series. It was found there, that in the absence of differential rotation, ideal modes (driven by gradients of B 0) become unstable for Ac ? 200 whereas resistive instabilities (generated by magnetic reconnection processes near critical levels, i.e. zeros of B0) require Ac ? 50. Here, Λ is the Elsasser number, a measure of the magnetic field strength and Λc is its critical value at marginal stability. Both types of instability can be stabilised by adding differential rotation into the system. For the resistive modes the exact form of the differential rotation is not important whereas for the ideal modes only a rotation rate which increases outward from the rotation axis has a stabilising effect. We found that in all cases which we investigated Λc increased rapidly and the modes disappeared when Rm ≈ O(ΛC), where the magnetic Reynolds number Rm is a measure of the strength of differential rotation. The main emphasis, however, is on instabilities which are driven by unstable gradients of the differential rotation itself, i.e. an otherwise stable fluid system is destabilised by a suitable differential rotation once the magnetic Reynolds number exceeds a certain critical value (Rm )c. Earlier work in the cylindrical geometry has shown that the differential rotation can generate an instability if Rm ) ?O(Λ). Those results, obtained for a fixed value of Λ = 100 are extended in two ways: to a spherical geometry and to an analysis of the effect of the magnetic field strength Λ on these modes of instability. Calculations confirm that modes driven by unstable gradients of the differential rotation can exist in a sphere and they are in good agreement with the local analysis and the predictions inferred from the cylindrical geometry. For Λ = O(100), the critical value of the magnetic Reynolds number (Rm )c Λ 100, depending on the choice of flow U0 . Modes corresponding to azimuthal wavenumber m = 1 are the most unstable ones. Although the magnetic field B 0 is itself a stable one, the field strength plays an important role for this instability. For all modes investigated, both for cylindrical and spherical geometries, (Rm )c reaches a minimum value for 50 ≈ Λ ≈ 100. If Λ is increased, (Rm )c ∝ Λ, whereas a decrease of Λ leads to a rapid increase of (Rm )c, i.e. a stabilisation of the system. No instability was found for Λ ≈ 10 — 30. Optimum conditions for instability driven by unstable gradients of the differential rotation are therefore achieved for ≈ Λ 50 — 100, Rm ? 100. These values lead to the conclusion that the instabilities can play an important role in the dynamics of the Earth's core. 相似文献
18.
19.
20.
V. M. Ovtchinnikov P. B. Kaazik D. N. Krasnoshchekov 《Izvestiya Physics of the Solid Earth》2012,48(3):211-221
Experimental data on the differential travel time t
BC–t
DF of seismic waves PKPDF and PKPBC in the Earth’s core under Africa and Australia are analyzed. The differential travel-time residuals beneath Africa in a narrow
range of angles from 21° to 25° between the direction of the seismic ray in the core and the Earth’s rotation axis exhibit
a scoop-shaped peculiarity not accounted for by cylindrical anisotropy in the inner core. A model with a 0.2–0.8% P-wave velocity anomaly with a radius of 1375 km in the cylindrical region in the outer core is proposed, which closely fits
the experimental data. We suggest that the velocity anomaly is generated by the dynamical processes occurring in the outer
core, namely, the growth of the inner core and the convection in the outer core, both leading to the formation of a low-density
anomaly in the outer core. 相似文献