共查询到20条相似文献，搜索用时 250 毫秒
1.
Andrew D. Gilbert 《地球物理与天体物理流体动力学》2013,107(1-4):241-258
Abstract An analysis of small-scale magnetic fields shows that the Ponomarenko dynamo is a fast dynamo; the maximum growth rate remains of order unity in the limit of large magnetic Reynolds number. Magnetic fields are regenerated by a “stretch-diffuse” mechanism. General smooth axisymmetric velocity fields are also analysed; these give slow dynamo action by the same mechanism. 相似文献
2.
Abstract This paper discusses dynamo action in generalisations of the Ponomarenko dynamo at large magnetic Reynolds number. The original Ponomarenko dynamo consists of a spiralling flow in which the stream surfaces are concentric cylinders of circular cross section, and the flow depends only on distance from the axis in cylindrical polar coordinates. In this study, the stream surfaces are allowed to be cylinders of arbitrary cross section, and the flow is only required to be independent of the coordinate along the cylinder axes. For smooth flows alpha and eddy diffusion effects are identified, in terms of the geometry of the stream surfaces, and asymptotic formulae for growth rates in the limit of large magnetic Reynolds number are obtained. Numerical support for these results is presented using direct simulation of dynamo action in selected flows at high conductivity. Finally the case is considered when in spherical polar coordinates the flow is independent of the azimuthal coordinate and the stream surfaces, which are tori, have arbitrary cross sections. 相似文献
3.
R. Kaiser 《地球物理与天体物理流体动力学》2013,107(1-2):125-135
Abstract Bayly (1993) introduced and investigated the equation (? t + v·▽-η ▽2)S = RS as a scalar analogue of the magnetic induction equation. Here, S(r, t) is a scalar function and the flow field v(r, t) and “stretching” function R(r, t) are given independently. This equation is much easier to handle than the corresponding vector equation and, although not of much relevance to the (vector) kinematic dynamo problem, it helps to study some features of the fast dynamo problem. In this note the scalar equation is considered for linear flow and a harmonic potential as stretching function. The steady equation separates into one-dimensional equations, which can be completely solved and therefore allow one to monitor the behaviour of the spectrum in the limit of vanishing diffusivity. For more general homogeneous flows a scaling argument is given which ensures fast dynamo action for certain powers of the harmonic potential. Our results stress the singular behaviour of eigenfunctions in the limit of vanishing diffusivity and the importance of stagnation points in the flow for fast dynamo action. 相似文献
4.
Krzysztof A. Mizerski 《地球物理与天体物理流体动力学》2013,107(1-2):218-243
We study the effect of stratification on large-scale dynamo action in convecting fluids in the presence of background rotation. The fluid is confined between two horizontal planes and both boundaries are impermeable, stress-free and perfectly conducting. An asymptotic analysis is performed in the limit of rapid rotation (τ???1 where τ is the Taylor number). We analyse asymptotic magnetic dynamo solutions in rapidly rotating systems generalising the results of Soward [A convection-driven dynamo I. The weak field case. Philos. Trans. R. Soc. Lond. A 1974, 275, 611–651] to include the effects of compressibility. We find that in general the presence of stratification delays the efficiency of large-scale dynamo action in this regime, leading to a reduction of the onset of dynamo action and in the nonlinear regime a diminution of the large-scale magnetic energy for flows with the same kinetic energy. 相似文献
5.
Abstract A simple mean-field model of a nonlinear stellar dynamo is considered, in which dynamo action is supposed to occur in a spherical shell, and where the only nonlinearity retained is the influence of the Lorentz forces on the zonal flow field. The equations are simplified by truncating in the radial direction, while full latitudinal dependence is retained. The resulting nonlinear p.d.e.'s in latitude and time are solved numerically, and it is found that while regular dynamo wave type solutions are stable when the dynamo number D is sufficiently close to its critical value, there is a wide variety of stable solutions at larger values of D. Furthermore, two different types of dynamo can coexist at the same parameter values. Implications for fields in late-type stars are discussed. 相似文献
6.
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
7.
Xing Wei 《地球物理与天体物理流体动力学》2015,109(2):159-167
We investigate numerically the kinematic dynamo induced by the superposition of two helical waves in a periodic box as a simplified model to understand the dynamo action in astronomical bodies. The effects of magnetic Reynolds number, wavenumber and wave frequency on the dynamo action are studied. It is found that this helical-wave dynamo is a slow dynamo. There exists an optimal wavenumber for the dynamo growth rate. A lower wave frequency facilitates the dynamo action and the oscillations of magnetic energy emerge at some particular wave frequencies. 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.
We present results from compressible Cartesian convection simulations with and without imposed shear. In the former case the dynamo is expected to be of α2 Ω type, which is generally expected to be relevant for the Sun, whereas the latter case refers to α2 dynamos that are more likely to occur in more rapidly rotating stars whose differential rotation is small. We perform a parameter study where the shear flow and the rotational influence are varied to probe the relative importance of both types of dynamos. Oscillatory solutions are preferred both in the kinematic and saturated regimes when the negative ratio of shear to rotation rates, q?≡??S/Ω, is between 1.5 and 2, i.e. when shear and rotation are of comparable strengths. Other regions of oscillatory solutions are found with small values of q, i.e. when shear is weak in comparison to rotation, and in the regime of large negative qs, when shear is very strong in comparison to rotation. However, exceptions to these rules also appear so that for a given ratio of shear to rotation, solutions are non-oscillatory for small and large shear, but oscillatory in the intermediate range. Changing the boundary conditions from vertical field to perfect conductor ones changes the dynamo mode from oscillatory to quasi-steady. Furthermore, in many cases an oscillatory solution exists only in the kinematic regime whereas in the nonlinear stage the mean fields are stationary. However, the cases with rotation and no shear are always oscillatory in the parameter range studied here and the dynamo mode does not depend on the magnetic boundary conditions. The strengths of total and large-scale components of the magnetic field in the saturated state, however, are sensitive to the chosen boundary conditions. 相似文献
10.
Giuseppina Nigro 《地球物理与天体物理流体动力学》2013,107(1-2):101-113
This article addresses the interesting and important problem of large-scale magnetic field generation in turbulent flows, using a self-consistent dynamo model recently developed. The main idea of this model is to consider the induction equation for the large-scale magnetic field, integrated consistently with the turbulent dynamics at smaller scales described by a magnetohydrodynamic shell model. The questions of dynamo action threshold, magnetic field saturation, magnetic field reversals, nature of the dynamo transition and the changes of small-scale turbulence as a consequence of the dynamo onset are discussed. In particular, the stability curve obtained by the model integration is shown in a very wide range of values of the magnetic Prandtl number not yet accessible by direct numerical simulation but more realistic for natural dynamos. Moreover, from our analysis it is shown that the large-scale dynamo transition displays a hysteretic behaviour and therefore a subcritical nature. The model successfully reproduces magnetic polarity reversals, showing the capability to generate persistence times which are increasing for decreasing magnetic diffusivity. Moreover, when the system reaches a statistically stationary dynamo state, where the large-scale magnetic field can abruptly reverse its polarity (magnetic reversal state) or not, keeping the same polarity (steady state), it shows an unmistakable tendency towards the energy equipartition for the turbulence at small scale. 相似文献
11.
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
12.
Rainer Beck 《地球物理与天体物理流体动力学》2013,107(1-3):3-4
Abstract Evidence from radio polarization measurements is reviewed that indicates that most galactic magnetic field structures fall into one of two categories: axisymmetric spiral and bisymmetric spiral. The resultant challenges to dynamo theorists is stated. Estimates of the magnetic field strengths based on equipartition of field and cosmic ray energies are given, but deviations from equipartition are inferred. Possible goals for future research are suggested. 相似文献
13.
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
14.
An inverse dynamo problem is presented in which we search for either kinematic dynamos which produce the same external magnetic fields or an invisible dynamo. The existence of flows which produce the same external magnetic fields is proved. However, we have not found general conditions necessary for such kind of dynamos. An “invisible dynamo” operates in an electrically conducting region surrounded by vacuum and generates a magnetic field trapped in the electrically conducting region so that no magnetic field exists in the vacuum. Invisible magnetic decay modes exist in cylinders, but no invisible growing field supported by the dynamo mechanism has been found. 相似文献
15.
Abstract In order to obtain a better insight into the excitation conditions of magnetic fields in flat objects, such as galaxies, we have calculated critical dynamo numbers of different magnetic field modes for spherical dynamos with a flat α-effect distribution. A simple but realistic approximation formula for the rotation curve is employed. In most cases investigated a stationary quadrupole-type solution is preferred. This is a consequence of the flat distribution of the α-effect. Non-axisymmetric fields are in all cases harder to excite than axisymmetric ones. This seems to be the case particularly for flat objects in combination with a realistic rotation curve for galaxies. The question of whether non-axisymmetric (bisymmetric) fields, which are observed in some galaxies, can be explained as dynamos generated by an axisymmetric αω-effect is therefore still open. 相似文献
16.
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
17.
Richard Wielebinski 《地球物理与天体物理流体动力学》2013,107(1-3):49-51
Abstract Observations are reviewed that indicate the existence of rotating rings in a number of galaxies that possess poloidal magnetic fields in their nuclear regions, including our own Galaxy. Jets from these, possibly aligned with the poloidal field, may also be present. The role of these rings in dynamo processes is briefly discussed. 相似文献
18.
Linear and nonlinear dynamo action is investigated for square patterns in nonrotating and weakly rotating Boussinesq Rayleigh-Bénard convection in a plane horizontal layer. The square-pattern solutions may or may not be symmetric to up-down reflections. Vertically symmetric solutions correspond to checkerboard patterns. They do not possess a net kinetic helicity and are found to be incapable of kinematic dynamo action at least up to magnetic Reynolds numbers of , 12 000. There also exist vertically asymmetric squares, characterized by rising (descending) motion in the centers and descending (rising) motion near the boundaries, among them such that possess full horizontal square symmetry and others lacking also this symmetry. The flows lacking both the vertical and horizontal symmetries possess kinetic helicity and show kinematic dynamo action even without rotation. The generated magnetic fields are concentrated in vertically oriented filamentary structures. Without rotation these dynamos are, however, always only kinematic, not nonlinear dynamos since the back-reaction of the magnetic field then forces the solution into the basin of attraction of a roll pattern incapable of dynamo action. But with rotation added parameter regions are found where stationary asymmetric squares are also nonlinear dynamos. These nonlinear dynamos are characterized by a subtle balance between the Coriolis and Lorentz forces. In some parameter regions also nonlinear dynamos with flows in the form of oscillating squares or stationary modulated rolls are found. 相似文献
19.
Yulia Krasheninnikova Alexander Ruzmaikin Dmitry Sokoloff Anvar Shukurov 《地球物理与天体物理流体动力学》2013,107(1-3):131-146
Abstract We discuss recent developments in the theory of large-scale magnetic structures in spiral galaxies. In addition to a review of galactic dynamo models developed for axisymmetric disks of variable thickness, we consider the possibility of dominance of non-axisymmetric magnetic modes in disks with weak deviations from axial symmetry. Difficulties of straightforward numerical simulation of galactic dynamos are discussed and asymptotic solutions of the dynamo equations relevant for galactic conditions are considered. Theoretical results are compared with observational data. 相似文献
20.
V. Urpin 《地球物理与天体物理流体动力学》2013,107(3-4):269-284
Abstract We consider the turbulent dynamo action in a differentially rotating flow by making use of a kinematic approach when the effect of a generated magnetic field on turbulent motions is neglected. The mean electromotive force is calculated in a quasilinear approximation. Differential rotation can stretch turbulent magnetic field lines and break the symmetry of turbulence in such a way that turbulent motions become suitable for the generation of a large scale magnetic field. The presence of shear changes the type of an equation governing the mean magnetic field. Due to shear stresses the mean magnetic field can be generated by a turbulent dynamo action even in a uniform turbulence. The growth rate depends on the length scale of the mean field being faster for the field with a smaller length scale. 相似文献