共查询到20条相似文献，搜索用时 31 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
2.
In order to gain a better understanding of the physical processes underlying fast dynamo action it is instructive to investigate the structure of both the magnetic field and the velocity field after the dynamo saturates. Previously, computational results have been presented (Cattaneo, Hughes and Kim, 1996) that indicate, in particular, that Lagrangian chaos is suppressed in the dynamical regime of the dynamo. Here we extend their model by removing the assumption of neglecting the inertial term. This allows for an investigation into the effect of this term on the evolution of the dynamo via a comparison of the two models. Our results indicate that this term plays a crucial role in the physics of the dynamo. 相似文献
3.
The most fundamental difficulty in the construction of an Earth-like dynamo model is associated with the constraint caused by the rapid rotation of the Earth. To stabilise numerical codes, many workers have introduced hyperviscosity into the governing equations. One of the major effects introduced by hyperviscosity is to offset the rotational constraint, and, consequently, to alter the key dynamics of an Earth-like dynamo. In this paper, an Earth-like convection model with or without the presence of an imposed magnetic field is investigated with or without the effect of hyperviscosity. A nonlinear dynamo model with the mean field approximation is also used to examine the dynamical effect of hyperviscosity. The results suggest that great care should be taken when hyperviscosity is employed in geodynamo models. 相似文献
4.
While rainfall intermittency is a dynamical phenomenon, little progress has been made in the literature on the link between rainfall intermittency and atmospheric dynamics. We present the basic dynamical models of intermittency that are phenomenologically most similar to rainfall: Pomeau–Manneville Type-III and On–Off. We then illustrate each type with both a 1-D iterative map and a corresponding stochastic process stressing the appearance of these dynamics in high-dimensional (stochastic) systems as opposed to low-dimensional chaotic systems. We show that the pdf of rainfall intensities, the pdf of “laminar phases” (periods of zero rainfall intensity), and the spectrum of the rainfall series all have power-law behavior that is broadly consistent with intermittency in the classic types. Using a seasonal analysis, we find that summer convective rainfall at daily and sub-daily scales seems consistent with features of Type-III intermittency. The correspondence with Type-III intermittency and a preliminary entropic analysis further suggest that rainfall may be an example of sporadic randomness, blending deterministic and stochastic components. 相似文献
5.
A nonlinear mean field dynamo in turbulent disks and spherical shells is discussed. We use a nonlinearity in the dynamo which includes the effect of delayed back-reaction of the mean magnetic field on the magnetic part of the — effect. This effect is determined by an evolutionary equation. The axisymmetric case is considered. An analytical expression (in a single-mode approximation) is derived which gives the magnitude of the mean magnetic field as a function of rotation and the parameters for turbulent disks. The value obtained for the mean magnetic field is in agreement with observations for galaxies. 相似文献
6.
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
7.
Abstract Our intent is to provide a simple and quantitative understanding of the variability of the axial dipole component of the geomagnetic field on both short and long time scales. To this end we study the statistical properties of a prototype nonlinear mean field model. An azimuthal average is employed, so that (1) we address only the axisymmetric component of the field, and (2) the dynamo parameters have a random component that fluctuates on the (fast) eddy turnover time scale. Numerical solutions with a rapidly fluctuating α reproduce several features of the geomagnetic field: (1) a variable, dominantly dipolar field with additional fine structure due to excited overtones, and sudden reversals during which the field becomes almost quadrupolar, (2) aborted reversals and excursions, (3) intervals between reversals having a Poisson distribution. These properties are robust, and appear regardless of the type of nonlinearity and the model parameters. A technique is presented for analysing the statistical properties of dynamo models of this type. The Fokker-Planck equation for the amplitude a of the fundamental dipole mode shows that a behaves as the position of a heavily damped particle in a bistable potential ∝(1 ? a 2)2, subject to random forcing. The dipole amplitude oscillates near the bottom of one well and makes occasional jumps to the other. These reversals are induced solely by the overtones. Theoretical expressions are derived for the statistical distribution of the dipole amplitude, the variance of the dipole amplitude between reversals, and the mean reversal rate. The model explains why the reversal rate increases with increasing secular variation, as observed. Moreover, the present reversal rate of the geodynamo, once per (2?3) × 105 year, is shown to imply a secular variation of the axial dipole moment of ～ 15% (about the current value). The theoretical dipole amplitude distribution agrees well with the Sint-800 data. 相似文献
8.
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
9.
Michael R. E. Proctor 《地球物理与天体物理流体动力学》2013,107(1):311-324
Abstract The kinematic dynamo problem is considered for certain steady velocity fields with symmetries that are plausible in a rapidly rotating convective system. By generalizing results proved for the mean field dynamo model by Proctor (1977a), it is shown that for a related “comparison problem” with modified boundary conditions, the eigenvalues are degenerate if there is no axisymmetric mean circulation, with modes of dipole and quadrupole parity excited with equal ease. The comparison problem can be shown to be closely similar to the dynamo problem when there is a region unfavourable to dynamo action surrounding the dynamo region. The near-symmetries found by Roberts (1972) for the mean field model are invoked to suggest that a close correspondence is likely even when this region is absent. It is therefore conjectured that such mean motions may be important in explaining the observed preference for solutions of dipole parity by planetary dynamos. 相似文献
10.
Tworkowski A. Covas E. Tavakol R. Brandenburg A. 《Studia Geophysica et Geodaetica》1998,42(3):350-355
Calculations for mean field dynamo models (in both full spheres and spherical shells), with both algebraic and dynamic -quenchings, show qualitative as well as quantitative differences and similarities in the dynamical behaviour of these models. We summarise and enhance recent results with extra examples.
Overall, the effect of using a dynamic appears to be complicated and is affected by the region of parameter space examined. 相似文献
11.
We investigate the dynamo underpinning of solar cycle precursor schemes based on direct or indirect measures of the solar surface magnetic field. We do so for various types of mean-field-like kinematic axisymmetric dynamo models, where amplitude fluctuations are driven by zero-mean stochastic forcing of the dynamo number controlling the strength of the poloidal source term. In all stochastically forced models considered, the surface poloidal magnetic field is found to have precursor value only if it feeds back into the dynamo loop, which suggests that accurate determination of the magnetic flux budget of the solar polar fields may hold the key to dynamo model-based cycle forecasting. 相似文献
12.
Andrew Phillips 《地球物理与天体物理流体动力学》2013,107(1-2):135-150
Abstract The asymptotic and the no-z approximation methods of solving the axisymmetric mean field αΩ dynamo equation in a galactic disc are compared. The behaviour of the solutions is explored in both the linear and nonlinear regimes for a variety of dynamo parameters and two different rotation curves. The solutions obtained from the two different approaches are found to be in good agreement. 相似文献
13.
Abstract The mean field induction equation of Steenbeck, Krause and Rädler (1966) is solved for anisotropic α ik -tensors of varying anisotropy. The attention is restricted to α2-dynamos in spheres with steady axisymmetric magnetic fields. The ratio of the electrical conductivity outside and inside the sphere is varied, but in all cases it is found that a steady dynamo does not exist when the anisotropy of the α ik -tensor exceeds a critical value. Such a critical value does not exist in the exceptional case of the Fermi boundary condition. The results emphasize the important effect of boundaries on the existence of solutions of the dynamo problem. 相似文献
14.
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
15.
Elstner D. Lesch H. von Linden Susane Otmianowska-Mazur Katarzyna Urbanik M. 《Studia Geophysica et Geodaetica》1998,42(3):373-381
In the present project we investigate the evolution of a three-dimensional (3D), large-scale galactic magnetic field under the influence of gas flows in spiral arms and in the presence of dynamo action. Our principal goal is to check how the dynamical evolution of gaseous spiral arms affects the global magnetic field structure and to what extent our models could explain the observed spiral patterns of polarization B-vectors in nearby galaxies. A two-step scheme is used: the N-body simulations of a two-component, self-gravitating disk provide the time-dependent velocity fields which are then used as the input to solve the mean-field dynamo equations.
We found that the magnetic field is directly influenced by large-scale non-axisymmetric density wave flows yielding the magnetic field locally well-aligned with gaseous spiral arms in a manner similar to that discussed already by Otmianowska-Mazur et al. 1997. However, an additional field amplification, introduced by a non-zero -term in the dynamo equations, is required to cause a systematic increase of magnetic energy density against the diffusive losses. Our simulated magnetic fields are also used to construct the models of a high-frequency (Faraday rotation-free) polarized radio emission accounting for effects of projection and limited resolution, thus suitable for direct comparisons with observations. 相似文献
16.
A survey is given on the present state of the geomagnetic dynamo theory which is based on the electrodynamics of mean fields in electrically conducting turbulent media. Models of both the 2-type and the ω-type are taken into consideration, i.e. models where the -effect alone, or together with a differential rotation, gives rise to the regeneration of magnetic fields. Results of special investigations are given and discussed. Models of the 2-type apply to the Earth provided that it shows no noticeable differential rotation. It is pointed out that such models can explain not only the generation of a magnetic field with an axisymmetric dipole-like structure, but also the occurrence of non-axisymmetric components and their westward drift. If, however, a noticeable differential rotation exists, models of the ω-type have to be envisaged. Such models also allow an understanding of the existence of a magnetic field with an axisymmetric dipole-like structure, but they do not provide for a straightforward interpretation of the occurrence and behaviour of the non-axisymmetric components. 相似文献
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19.
O. Goepfert 《地球物理与天体物理流体动力学》2019,113(1-2):222-234
ABSTRACTIt is shown that flows in precessing cubes develop at certain parameters large axisymmetric components in the velocity field which are large enough to either generate magnetic fields by themselves, or to contribute to the dynamo effect if inertial modes are already excited and acting as a dynamo. This effect disappears at small Ekman numbers. The critical magnetic Reynolds number also increases at low Ekman numbers because of turbulence and small-scale structures. 相似文献
20.
Abstract We investigated global axisymmetric (m = 0) and non-axisymmetric (m = 1) modes of magnetic fields generated by the galactic dynamo including the α2-dynamo. The α2-dynamo is responsible for the field generation in the central region of galaxies where the shear of galactic rotation is weak (e.g. M51). The highest growth rate of m = 1 modes is always smaller than that of m = 0 modes; thus m = 1 modes of the standard galactic dynamo cannot explain the dominance of the bisymmetric fields in spiral galaxies. Radial extent of each m = 1 mode is too narrow to reproduce the observed bisymmetric structure extending over a disk. 相似文献