共查询到20条相似文献，搜索用时 31 毫秒
1.
Abstract In this paper a method for solving the equation for the mean magnetic energy <BB> of a solar type dynamo with an axisymmetric convection zone geometry is developed and the main features of the method are described. This method is referred to as the finite magnetic energy method since it is based on the idea that the real magnetic field B of the dynamo remains finite only if <BB> remains finite. Ensemble averaging is used, which implies that fields of all spatial scales are included, small-scale as well as large-scale fields. The method yields an energy balance for the mean energy density ε ≡ B 2/8π of the dynamo, from which the relative energy production rates by the different dynamo processes can be inferred. An estimate for the r.m.s. field strength at the surface and at the base of the convection zone can be found by comparing the magnetic energy density and the outgoing flux at the surface with the observed values. We neglect resistive effects and present arguments indicating that this is a fair assumption for the solar convection zone. The model considerations and examples presented indicate that (1) the energy loss at the solar surface is almost instantaneous; (2) the convection in the convection zone takes place in the form of giant cells; (3) the r.m.s. field strength at the base of the solar convection zone is no more than a few hundred gauss; (4) the turbulent diffusion coefficient within the bulk of the convection zone is about 1014cm2s?1, which is an order of magnitude larger than usually adopted in solar mean field models. 相似文献
2.
Abstract A spherical αω-dynamo is studied for small values of the viscous coupling parameter ε ～ v1/2, paying attention particularly to large dynamo numbers. The present study is a follow-up of the work by Hollerbach et al. (1992) with their choice of α-effect and Archimedean wind including also the constraint of magnetic field symmetry (or antisymmetry) due to equatorial plane. The magnetic field scaled by ε1/2 is independent of ε in the solutions for dynamo numbers smaller than a certain value of D b (the Ekman state) which are represented by dynamo waves running from pole to equator or vice-versa. However, for dynamo numbers larger than D b the solution bifurcates and subsequently becomes dependent on ε. The bifurcation is a consequence of a crucial role of the meridional convection in the mechanism of magnetic field generation. Calculations suggest that the bifurcation appears near dynamo number about 33500 and the solutions for larger dynamo numbers and ε = 0 become unstable and fail, while the solutions for small but non-zero ε are characterized by cylindrical layers of local maximum of magnetic field and sharp changes of geostrophic velocity. Our theoretical analysis allows us to conclude that our solution does not take the form of the usual Taylor state, where the Taylor constraint should be satisfied due to the special structure of magnetic field. We rather obtained the solution in the form of a “weak” Taylor state, where the Taylor constraint is satisfied partly due to the amplitude of the magnetic field and partly due to its structure. Calculations suggest that the roles of amplitude and structure are roughly fifty-fifty in our “weak” Taylor state solution and thus they can be called a Semi-Taylor state. Simple estimates show that also Ekman state solutions can be applicable in the geodynamo context. 相似文献
3.
Abstract We discuss the steady states of the αω-dynamo in a thin disc which arise due to α-quenching. Two asymptotic regimes are considered, one for the dynamo numberD near the generation thresholdD 0, and the other for |D| ? 1. Asymptotic solutions for |D—D 0| ? |D 0| have a rather universal character provided only that the bifurcation is supercritical. For |D| ? 1 the asymptotic solution crucially depends on whether or not the mean helicity α, as a function ofB, has a positive root (hereB is the mean magnetic field). When such a root exists, the field value in the major portion of the disc is O(l), while near the disc surface thin boundary layers appear where the field rapidly decreases to zero (if the disc is surrounded by vacuum). Otherwise, when α = O(|B|?s) for |B| → ∞, we demonstrate that |B| = O(|D|1/s ) and the solution is free of boundary layers. The results obtained here admit direct comparison with observations of magnetic fields in spiral galaxies, so that an appropriate model of nonlinear galactic dynamos hopefully could be specified. 相似文献
4.
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
5.
Abstract In this paper we analyse the stationary mean energy density tensor Tij = BiBj for the x 2-sphere. This model is one of the simplest possible turbulent dynamos, originally due to Krause and Steenbeck (1967): a conducting sphere of radius R with homogeneous, isotropic and stationary turbulent convection, no differential rotation and negligible resistivity. The stationary solution of the (linear) equation for Tij is found analytically. Only Trr , T θθ and T φφ are unequal to zero, and we present their dependence on the radial distance r. The stationary solution depends on two coefficients describing the turbulent state: the diffusion coefficient β≈?u2?τc/3 and the vorticity coefficient γ ≈ ?|?×u|2?τc/3 where u(r, t) is the turbulent velocity and c its correlation time. But the solution is independent of the dynamo coefficient α≈??u·?×u?τc/3 although α does occur in the equation for Tij . This result confirms earlier conclusions that helicity is not required for magnetic field generation. In the stationary state, magnetic energy is generated by the vorticity and transported to the boundary, where it escapes at the same rate. The solution presented contains one free parameter that is connected with the distribution of B over spatial scales at the boundary, about which Tij gives no information. We regard this investigation as a first step towards the analysis of more complicated, solar-type dynamos. 相似文献
6.
Abstract The solution of the full nonlinear hydromagnetic dynamo problem is a major numerical undertaking. While efforts continue, supplementary studies into various aspects of the dynamo process can greatly improve our understanding of the mechanisms involved. In the present study, the linear stability of an electrically conducting fluid in a rigid, electrically insulating spherical container in the presence of a toroidal magnetic field Bo(r,θ)lø and toroidal velocity field Uo(r,θ)lø, [where (r,θ,ø) are polar coordinates] is investigated. The system, a model for the Earth's fluid core, is rapidly rotating, the magnetostrophic approximation is used and thermal effects are excluded. Earlier studies have adopted a cylindrical geometry in order to simplify the numerical analysis. Although the cylindrical geometry retains the fundamental physics, a spherical geometry is a more appropriate model for the Earth. Here, we use the results which have been found for cylindrical systems as guidelines for the more realistic spherical case. This is achieved by restricting attention to basic states depending only on the distance from the rotation axis and by concentrating on the field gradient instability. We then find that our calculations for the sphere are in very good qualitative agreement both with a local analysis and with the predictions from the results of the cylindrical geometry. We have thus established the existence of field gradient modes in a realistic (spherical) model and found a sound basis for the study of various other, more complicated, classes of magnetically driven instabilities which will be comprehensively investigated in future work. 相似文献
7.
Abstract In order to show that aperiodic magnetic cycles, with Maunder minima, can occur naturally in nonlinear hydromagnetic dynamos, we have investigated a simple nonlinear model of an oscillatory stellar dynamo. The parametrized mean field equations in plane geometry have a Hopf bifurcation when the dynamo number D=1, leading to Parker's dynamo waves. Including the nonlinear interaction between the magnetic field and the velocity shear results in a system of seven coupled nonlinear differential equations. For D>1 there is an exact nonlinear solution, corresponding to periodic dynamo waves. In the regime described by a fifth order system of equations this solution remains stable for all D and the velocity shear is progressively reduced by the Lorentz force. In a regime described by a sixth order system, the solution becomes unstable and successive transitions lead to chaotic behaviour. Oscillations are aperiodic and modulated to give episodes of reduced activity. 相似文献
8.
Magnetic instability in a rapidly rotating cylindrical annulus with a finitely conducting inner core
C. J. Lamb 《地球物理与天体物理流体动力学》2013,107(2-4):227-250
Abstract We consider the stability of a toroidal magnetic field B = B(s*) (where (s*,φ,z*) are cylindrical polar coordinates) in a cylindrical annulus of conducting fluid with inner and outer radii si and s o rotating rapidly about its axis. The outer boundary is taken to be either insulating or perfectly conducting, and the effect of a finite magnetic diffusivity in the inner core is investigated. The ratio of magnetic diffusivity in the inner core to that of the outer core is denoted by ηη→0 corresponding to a perfectly conducting inner core and η→∞ to an insulating one. Comparisons with the results of Fearn (1983b, 1988) were made and a good match found in the limits η→0 and η→∞ with his perfectly conducting and insulating results, respectively. In addition a new mode of instability was found in the eta;→0 regime. Features of this new mode are low frequency (both the frequency and growth rate →0 as η→0) and penetration deep into the inner core. Typically it is unstable at lower magnetic field strengths than the previously known instabilities. 相似文献
9.
Variations in the photospheric magnetic field in the region of solar flares, related to halo coronal mass ejections (HCMEs) with velocities V > 1500, 1000 < V < 1500, and V < 650 km/s, have been studied based on SOHO/MDI data. Using data with a time resolution of 96 min, it has been indicated that on average the ??B L?? and ??|B L|?? field characteristics increase nonmonotonically during 1?C1.5 days before a flare and decrease during 0.5?C1 days after a flare for groups of ejections with V > 1000 km/s for all considered HCME groups. Angle brackets designate averaging of the measured B L magnetic field component and its magnitude |B L| within an area with specified dimensions and the center coincident with the projection onto the region where the flare center field is measured. It has been established that a solar flare related to an HCME originates when the ??B L?? and ??|B L|?? values are larger than the boundary values in the flare region. Based on 1-min data, it has been found for several HCMEs with V > 1500 km/s that the beginning of powerful flares related to ejections is accompanied by rapid impulsive or stepped variations in ??B L?? and ??|B L|?? near the center of a flare with a size of approximately 4.5°. It has been established that the HCME velocity positively correlates with the |??B L??| value at the flare onset. 相似文献
10.
11.
David R. Fearn 《地球物理与天体物理流体动力学》2013,107(3):227-239
Abstract In part I of this study (Fearn, 1983b), instabilities of a conducting fluid driven by a toroidal magnetic field B were investigated. As well as confirming the results of a local stability analysis by Acheson (1983), a new resistive mode of instability was found. Here we investigate this mode in more detail and show that instability exists when B(s) has a zero at some radius s=s c. Then (in the limit of small resistivity) the instability is concentrated in a critical layer centered on s c . The importance of the region where B is small casts some doubt on the validity of the simplifications made to the momentum equation in I. Calculations were therefore repeated using the full momentum equation. These demonstrate that the neglect of viscous and inertial terms when the mean field is strong does not lead to spurious results even when there are regions where B is small. 相似文献
12.
Summary Magnetic field structures at great distances from the Sun have been analyzed qualitatively for a simple vacuum reconnection model of the interplanetary and interstellar magnetic field. In dependence on the mutual orientation of the main solar dipole s and the local interstellar fieldB
0
, either an open or closed configuration of the large-scale field is formed. For(s
B
0
)>0, the field lines are represented by a system of magnetic lines open towards interstellar space. In the case of(s
B
0
)<0 there exist two zero-points and a separating surface below the heliopause separating the open lines of the interstellar field from the closed lines of the interplanetary field. The magnetic field configuration is characterized by a certain asymmetry, which is considered for(s
B
0
)=0. 相似文献
13.
Small-scale (scales of ∼0.5–256 km) electric fields in the polar cap ionosphere are studied on the basis of measurements of
the Dynamics Explorer 2 (DE-2) low-altitude satellite with a polar orbit. Nineteen DE-2 passes through the high-latitude ionosphere
from the morning side to the evening side are considered when the IMF z component was southward. A rather extensive polar cap, which could be identified using the ɛ-t spectrograms of precipitating particles with auroral energies, was formed during the analyzed events. It is shown that the
logarithmic diagrams (LDs), constructed using the discrete wavelet transform of electric fields in the polar cap, are power
law (μ ∼ s
α). Here, μ is the variance of the detail coefficients of the signal discrete wavelet transform, s is the wavelet scale, and index α characterizes the LD slope. The probability density functions P(δE, s) of the electric field fluctuations δE observed on different scales s are non-Gaussian and have intensified wings. When the probability density functions are renormalized, that is constructed
of δE/s
γ, where γ is the scaling exponent, they lie near a single curve, which indicates that the studied fields are statistically
self-similar. In spite of the fact that the amplitude of electric fluctuations in the polar cap is much smaller than in the
auroral zone, the quantitative characteristics of field scaling in the two regions are similar. Two possible causes of the
observed turbulent structure of the electric field in the polar cap are considered: (1) the structure is transferred from
the solar wind, which is known to have turbulent properties, and (2) the structure is generated by convection velocity shears
in the region of open magnetic field lines. The detected dependence of the characteristic distribution of turbulent electric
fields over the polar cap region on IMF B
y
and the correlation of the rms amplitudes of δE fluctuations with IMF B
z
and the solar wind transfer function (B
y
2 + B
z
2)1/2sin(θ/2), where θ is the angle between the geomagnetic field and IMF reconnecting on the dayside magnetopause when IMF B
z
< 0, together with the absence of dependence on the IMF variability are arguments for the second mechanism. 相似文献
14.
Glenn R. Ierley 《Physics of the Earth and Planetary Interiors》1984,36(1):43-48
Virtually all dynamo models may be expected to give rise to a permanent differential rotation between mantle and core. Weak conductivity in the mantle permits small leakage currents which couple to the radial component of the magnetic field, producing a Lorentz torque. Mechanical equilibrium is achieved when a zero net torque is established at a critical rotation rate. An estimate of the drift is determined easily given the magnetic field structure predicted by any dynamo model. The result for the drift rate at the core-mantle interface along the equator is given by the product of three factors The first of these is a geometrical factor which depends only on the structural character of the field. For a variety of model fields, this factor ranges from 16 to 35. The second factor is the ratio of r.m.s. toroidal to poloidal field. This ratio is an (implicitly) adjustable parameter of both α2 and α-ω dynamos, and is a measure of the relative efficiency of the generation process for each component. The third (dimensional) term is the ratio of core magnetic diffusivity to core radius, 10?4 cm s?1.The result is essentially independent of the value of mantle diffusivity and its effective depth. The sign of the result may be positive or negative. For α2 dynamos a westward drift is produced by choosing α > 0 in the Northern Hemisphere, which constitutes a dynamical assertion about the dynamo process. For an r.m.s. toroidal field of the order of 15 Gs, based on fairly general considerations, a drift rate comparable to observation is expected. 相似文献
15.
A crucial step in the investigation of the energetics of motions in the Earth's core and the generation of the geomagnetic field by the hydromagnetic dynamo process is the estimation of the average strength of the magnetic field B = Bp + BT in the core. Owing to the probability that the toroidal field BT in the core, which has no radial component, is a good deal stronger than the poloidal field Bp, direct downward extrapolation of the surface field to the core-mantle interface gives no more than an extreme lower limit to . This paper outlines the indirect methods by which can be estimated, arguing that is probably about 10?2 T (100 Γ) but might be as low as 10?3 T (10 Γ) or as high as 5 × 10?2 T (500 Γ). 相似文献
16.
R. Hide 《地球物理与天体物理流体动力学》2013,107(1):171-176
Abstract A method has recently been proposed for finding the radius rc of the electrically-conducting fluid core of a planet of outer radius rs from observations of the magnetic field B in the accessible region near or well above the surface of the planet (Hide, 1978). The method is based on the supposition that when the magnetic field is produced by hydromagnetic dynamo action in the core, implying that the magnetic Reynolds number R there is large, (a) fluctuations in B can occur everywhere on the comparatively short advective time-scale τ A associated with fluid motions in the core and so can fluctuations in the quantity N, defined for any closed surface S as the total number of intersection of magnetic lines of force with S, provided that S lies well outside the core, but (b) at the surface of the core, where lines of magnetic force emerge from their region of origin, concomitant fluctuations in N are negligibly small, of the order of τ A/τO where τ O (= RτA ) is the Ohmic decay time of the core. A proof of this supposition follows directly from the general expression derived in the present paper showing that when S is a material surface the time rate of change of N is equal to minus twice the line integral of the current density divided by the electrical conductivity around all the lines on S where the magnetic field is tangential to S. This expression (which Palmer in an accompanying paper rederives and extends to the relativistic case using the mathematical formalism of Cartan’s exterior calculus) also provides a direct demonstration of the well-known result that although high electrical conductivity, sufficient to make R ? 1, is a necessary condition for hydromagnetic dynamo action, such action is impossible in a perfect conductor, when R→ ∞. 相似文献
17.
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
18.
Edward R. Benton 《地球物理与天体物理流体动力学》2013,107(1):345-358
Abstract An explicit example of a steady prototype Lortz dynamo is elaborated in terms of a previously derived illustrative, exact, closed form solution to the nonlinear dynamo equations. The eigenvalue character of the dynamo problem is now introduced which simplifies the solution. The magnetic field lines, which lie on circular cylinders, and velocity streamline pattern are then displayed and discussed. Analysis of the magnetic energy balance by way of the Poynting flux reveals the existence of a finite critical cylinder across which zero net magnetic energy flows, thereby proving that the material inside is a self-excited dynamo, despite the fact that the total magnetic energy is unbounded. 相似文献
19.
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
20.
N. Yokoi 《地球物理与天体物理流体动力学》2013,107(1-2):114-184
The turbulent cross helicity is directly related to the coupling coefficients for the mean vorticity in the electromotive force and for the mean magnetic-field strain in the Reynolds stress tensor. This suggests that the cross-helicity effects are important in the cases where global inhomogeneous flow and magnetic-field structures are present. Since such large-scale structures are ubiquitous in geo/astrophysical phenomena, the cross-helicity effect is expected to play an important role in geo/astrophysical flows. In the presence of turbulent cross helicity, the mean vortical motion contributes to the turbulent electromotive force. Magnetic-field generation due to this effect is called the cross-helicity dynamo. Several features of the cross-helicity dynamo are introduced. Alignment of the mean electric-current density J with the mean vorticity Ω , as well as the alignment between the mean magnetic field B and velocity U , is supposed to be one of the characteristic features of the dynamo. Unlike the case in the helicity or α effect, where J is aligned with B in the turbulent electromotive force, we in general have a finite mean-field Lorentz force J ?×? B in the cross-helicity dynamo. This gives a distinguished feature of the cross-helicity effect. By considering the effects of cross helicity in the momentum equation, we see several interesting consequences of the effect. Turbulent cross helicity coupled with the mean magnetic shear reduces the effect of turbulent or eddy viscosity. Flow induction is an important consequence of this effect. One key issue in the cross-helicity dynamo is to examine how and how much cross helicity can be present in turbulence. On the basis of the cross-helicity transport equation, its production mechanisms are discussed. Some recent developments in numerical validation of the basic notion of the cross-helicity dynamo are also presented. 相似文献