共查询到20条相似文献，搜索用时 46 毫秒
1.
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
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ABSTRACTThe magnetic fields in the inner parts of some spiral galaxies are understood quite well. Their generation is connected with the dynamo mechanism that is based on the joint action of turbulent diffusion and the α-effect. Usually the galactic dynamo is described with the so-called no-z approximation which takes into account that the galaxy disc is quite thin, with the implication that some spatial derivatives may be replaced by algebraic expressions. Some galaxies have outer rings that are situated at some distance from the galactic centre. The magnetic field can be described there also using the no-z model. As the thickness of such objects is comparable with their width, it is necessary to take into account the z-dependence of the field. We have studied the magnetic field evolution using the no-z approximation and torus dynamo model for the torus with rectangular cross-section in the axisymmetric case. 相似文献
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Nathan Blaunstein 《Annales Geophysicae》1995,13(6):617-626
In contrast to the way that the spreading of irregularities in a plasma is usually considered, the diffusion spreading of irregularities stretched along the geomagnetic field B is examined using a three-dimensional rigorous numerical model of quasi-neutral diffusion in the presence of a magnetic field, in conjunction with the actual height variations of the diffusion and conductivity tensors in the ionosphere. A comparison with the earlier constructed approximate model of unipolar diffusion was made. As in the previous case, the same peculiarities of irregularity spreading in the inhomogeneous background ionospheric plasma were observed. The accuracy of the approximate model for describing the process of spreading of anisotropic ionospheric irregularities is established. Time relaxation effects of real heating-induced ionospheric irregularities on their scale transverse to B are presented using the approximate analytical model for the case of a quasi-homogeneous ionospheric plasma. The calculated results have a vivid physical meaning and can be directly compared with experimental data on the radiophysical observations of artificial heating-induced irregularities created by powerful radio waves in the ionosphere. 相似文献
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Abstract Unsteady fast dynamos are constructed using a sequence of rapid movements separated by periods of diffusion of the magnetic field. Motivated by the physical mechanism described by Ze'dovich and by Soward, we examine the effect of single-mode Beltrami waves applied sequentially, and show that they can be approximated by a simple “stretch-fold-shear” (SFS) map of the unit cube onto itself. In the SFS map, the field points in a fixed direction and diffusion is easily computed. The numerical results indicate that fast dynamo action occurs for sufficiently large shear, and that the process is primarily a coherent feature of the larger magnetic scales. Similar results are obtained for smooth flows. Some preliminary analysis of the SFS map using a decomposition method is described. 相似文献
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H. U. Schmidt 《地球物理与天体物理流体动力学》2013,107(1-4):249-270
Abstract Some examples of research on structure and formation of sunspots are briefly recollected in historical sequence. They relate to many facets of sunspots, first: magnetic inhibition of convection, the conjecture of a fiat penumbra, the stratification beneath the umbra, the observable magnetic profile, the Evershed effect as syphon flow, the concept of a magnetopause; next: cooling by Alfven waves, evolution and stability, the “bright ring”, the observed change of umbra brightness with the phase of the sunspot cycle, the hypothetical cluster of separate flux strands underneath the umbra, the profile of the magnetopause, the structure of the penumbra and the inclination of its field and finally: the concept of a deep penumbra with volume currents, exchange convection and the concept of a second current sheet separating umbra and penumbra. Of course, the rigorous theoretical modeling of local magnetoconvection is an essential tool for our understanding of all these processes. I do not deal with it here, but the reader has a fascinating review of magnetoconvection already in his hands (Weiss, 1991). 相似文献
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Abstract In this paper we consider the propagation of magneto-acoustic-gravity waves in a compressible, conducting isothermal atmosphere permeated by a uniform horizontal magnetic field. The singular levels, arising in a horizontal magnetic field, are considered in their most general form. Exact analytical solutions for a number of particular cases of wave propagation are obtained. The wave transformation is analyzed for all these cases using the solutions obtained. Based on the theory of wave propagation across a magnetic field, low-frequency wave trapping in a chromospheric resonator is explained, and some properties of running penumbral waves are discussed. 相似文献
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Bashir W. Sharif 《地球物理与天体物理流体动力学》2013,107(6):493-511
In this article we study the linear instability of the two-dimensional strongly stratified model for global MHD in the diffusive solar tachocline. Gilman and Fox [Gilman, P.A. and Fox, P., Joint instability of the latitudinal differential rotation and toroidal magnetic fields below the solar convection zone. Astrophys. J., 1997, 484, 439–454] showed that for ideal MHD, the observed surface differential rotation becomes more unstable than is predicted by Watson's [Watson, M., Shear instability of differential rotation in stars. Geophys. Astrophys. Fluid Dyn., 1981, 16, 285–298] nonmagnetic analysis. They showed that the solar differential rotation is unstable for essentially all reasonable values of the differential rotation in the presence of an antisymmetric toroidal field. They found that for the broad field case B φ～sinθcosθ, θ being the co-latitude, instability occurs only for the azimuthal m?=?1 mode, and concluded that modes which are symmetric (meridional flow in the same direction) about the equator onset at lower field strengths than the antisymmetric modes. We study the effect of viscosity and magnetic diffusivity in the strongly stably stratified case where diffusion is primarily along the level surfaces. We show that antisymmetric modes are now strongly preferred over symmetric modes, and that diffusion can sometimes be destabilising. Even solid body rotation can be destabilised through the action of magnetic field. In addition, we show that when diffusion is present, instability can occur when the longitudinal wavenumber m?=?2. 相似文献
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The paper deals with the dynamo action of the Roberts flow, that is, a flow depending periodically on two cartesian coordinates, X and Y , but being independent of the third one, Z . In particular the case is considered in which the magnetic fields, which are periodic in X, Y and Z , have period lengths in the XY -plane being integer multiples of that of the flow. Two approaches are used. Firstly, the equations governing the magnetic field are reduced to a matrix eigenvalue problem, which is solved numerically. Secondly, a mean magnetic field is defined by averaging over proper areas in the XY -plane, corresponding equations are derived, in which the induction effect of the flow occurs as an anisotropic f -effect, and analytic solutions are given. The results are of particular interest for the Karlsruhe dynamo experiment, which works with a Roberts type flow consisting of 52 cells inside a cylindrical volume. In order to check the reliability of predictions concerning self-excitation based on the mean-field approach, analogous predictions are derived for a rectangular box containing 50 cells, and are compared with results obtained with the help of direct solutions of the eigenvalue problem mentioned. It turns out that the simple mean-field approach in general underestimates the requirements for self-excitation. The corresponding results agree with those obtained in the subharmonic approach only if the side length L of the box, its height H and the edge length l of a spin generator satisfy $ L \gg H \gg l $ . In Appendix B, some comments on previous results concerning $\cal {ABC}$ dynamos are made in the light of the subharmonic formalism used in the paper. 相似文献
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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
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Abstract The Lagrangian approach to turbulent diffusion is considered through an improved Langevin model approach. The improved model partially accounts for the interaction between pressure and viscous stresses, an interaction not included in previous studies. The model is used to obtain one and two particle dispersion relations and it permits calculation of Eulerian-Lagrangian scale relations. Turbulence Reynolds number and time span limits for Richardson's law of diffusion are obtained. Non-stationarity of the acceleration between two particles is discussed as it relates to Richardson's law and the conclusions are considered in view of both laboratory and geophysical fluid dynamical data. 相似文献
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Vladimir Priklonsky Anvar Shukurov Dmitry Sokoloff Andrew Soward 《地球物理与天体物理流体动力学》2013,107(1-2):97-114
Abstract We reconsider thin-disc global asymptotics for kinematic, axisymmetric mean-field dynamos with vacuum boundary conditions. Non-local terms arising from a small but finite radial field component at the disc surface are consistently taken into account for quadrupole modes. As in earlier approaches, the solution splits into a local part describing the field distribution along the vertical direction and a radial part describing the radial (global) variation of the eigenfunction. However, the radial part of the eigenfunction is now governed by an integro-differential equation whose kernel has a weak (logarithmic) singularity. The integral term arises from non-local interactions of magnetic fields at different radii through vacuum outside the disc. The non-local interaction can have a stronger effect on the solution than the local radial diffusion in a thin disc, however the effect of the integral term is still qualitatively similar to magnetic diffusion. 相似文献
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S. V. Starchenko 《地球物理与天体物理流体动力学》2019,113(1-2):71-79
ABSTRACTNumerical models of planetary MHD dynamos have led to many advances in the last twenty years. However, the accessible parameter space of these models is somewhat limited due to computational constraints. A number of numerically based scaling laws have been proposed, but it has been difficult to reliably confirm them from the simulation data alone. Since these scaling laws have to be used to extend the numerical models into the planetary parameter regime, getting correct scalings is an important issue. Here some possible balances between the relevant terms in the dynamo equations are considered, and a number of different known and new scaling laws are proposed and justified from analytical point of view. Some of these laws are compatible with the widely known Christensen and Aubert (Geophys. J. Int. 2006, 166) scaling for the magnetic field strength. Plausible estimates of the typical values of the important quantities in the Earth's core and other Terrestrial planets are made, and the extent to which the various scaling laws are consistent with these estimates is discussed. 相似文献
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Marita Krause 《地球物理与天体物理流体动力学》2013,107(1-3):23-26
Abstract Methods of estimating the strength and direction of galactic magnetic fields from radio polarization measurements are reviewed. Particular attention is paid to the analysis of the Faraday rotation in order to derive the large scale magnetic field structure. Ways in which an axisymmetric spiral field structure can be observationally distinguished from a bisymmetric spiral structure are described, as are the ways in which field symmetric with respect to the galactic plane can be distinguished from those that are antisymmetric. 相似文献
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Arnab Rai Choudhuri 《地球物理与天体物理流体动力学》2013,107(3-4):261-291
Abstract We study the problem of the coalescence of twisted flux tubes by assuming that the azimuthal field lines reconnect at a current sheet during the coalescence process and everywhere else the magnetic field is frozen in the fluid. We derive relations connecting the topology of the coalesced flux tube with the topologies of the initial flux tubes, and then obtain a structure equation for calculating the field configuration of the coalesced flux tube from the given topology. Some solutions for the two extreme cases of low-β plasma and high-β plasma are discussed. The coalesced flux tube has less twist than the initial flux tube. Magnetic helicity is found to be exactly conserved during the coalescence, but the assumptions in the model put a constraint on the energy dissipation so that we do not get a relaxation to the minimum-energy Taylor state in the low-β case. It is pointed out that the structure equation connecting the topology and the equilibrium configuration is quite general and can be of use in many two-dimensional flux tube problems. 相似文献
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Jürgen Reichert 《地球物理与天体物理流体动力学》2013,107(3-4):213-226
Abstract A spherical mean-field dynamo model is considered in which both the mean motion and the mean electro-motive force due to fluctuating motions show some spherical symmetry. It is shown that under some reasonable assumptions the magnetic field is bound to decay to zero. 相似文献
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Abstract The structure and collapse of linear three-dimensional magnetic neutral points is studied by varying the four parameters (p, q,j|,j⊥ ) that define, in general, the linear field of a neutral point. The effect of these parameters on both the skeleton structure (i.e. the fan and spine) and the actual field line structure of the null is considered. It is found that one current component (j⊥ ) causes the skeleton structure of the null to fold up from its potential state, whereas the other current component (j |;) causes the field lines to bend. The two other parameters (p,q) determine the potential structure of the null and cause the null to transform from a three-dimensional null to a two-dimensional null and from a positive (type B) null to a negative (type A) null. To investigate the collapse of three-dimensional nulls, solutions to the linear, low-β ideal magnetohydrodynamic equations are found. It is found that three-dimensional null points can collapse if the field line foot-points are free and energy can propagate into the system. 相似文献
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Mitchell A. Berger 《地球物理与天体物理流体动力学》2013,107(1-2):79-104
Abstract The Cauchy-Schwarz inequality is employed to find geometry-independent limits on the magnetic helicity dissipation rate in a resistive plasma. These limits only depend upon the total energy of the plasma, the energy dissipation rate, and a mean diffusion coefficient. For plasmas isolated from external energy sources, limits can also be set on the minimum time necessary to dissipate a net amount of helicity ΔH. As evaluated in the context of a solar coronal loop, these limits strongly suggest that helicity decay occurs on a diffusion timescale which is far too great to be relevant to most coronal processes. Furthermore, rapid reconnection is likely to approximately conserve magnetic helicity. The dilliculties involved in determining the free energy residing in a magnetic structure (given the constraint of magnetic helicity conservation) are discussed. 相似文献
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I. A. Kerimov 《Izvestiya Physics of the Solid Earth》2009,45(5):444-460
The basic theoretical foundations of the spectral analysis of gravity and magnetic data based on the approximation approach have been considered and corresponding expressions implementing various statements of the F-approximation method have been derived [Strakhov and Kerimov, 1999; 2000; 2001]. The author considered the algorithms and computer implementation of the F-approximation of anomalous gravity and magnetic fields presented in the results of testing with the use of a number of model examples and data on the accuracy of the model field approximation earlier on in [Kerimov, 2003]. In this paper, I consider methodological features of constructing the F-approximation from the detailed gravity and magnetic surveys, anomalous gravity and magnetic fields reconstructed with the use of the F -approximation, and examples of the field transforms obtained with the use of this approach. 相似文献