ISSN:0309-1929    

DOI:10.1080/03091928908243459

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Recently Galloway and Frisch (1986) have reported numerical results for kinematic dynamos caused by steady spatially periodic flows at large magnetic Reynolds number,Rm. For their special case of two-dimensional (z*-independent) motion, the asymptotic theory developed by Childress (1979) is valid as Rm→∞. According to that theory models of given z*-wave number,j*, grow at a rate,p*, proportional toRm−½. This power law behaviour was not isolated by Galloway and Frisch (1986), who considered values ofRmup to 1500. Nevertheless, their numerical values forp* agree well with the asymptotic theory developed by Soward (1987). That asymptotic theory, which depends upon a second expansion parameter linked toj*, is outlined briefly. It shows that the ChildressRm−½-power law is achieved in the limitj*(Rm−½InRm)→0. Moreover, when the results of the double expansion are applied to the Galloway and Frischj* equals;2 model, for which detailed results are available, it is clear thatRm−½-power law is achieved only whenRmexceeds approximately 104.

ISSN:0309-1929    

DOI:10.1080/03091928908243460

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

In this paper we show that the adjoint formulation of the Stretch-Fold-Shear (SFS) fast dynamo model has smooth eigenfunctions at zero diffusivity. We thus compute fast dynamo action with smooth fields. We note that the adjoint problem is equivalent to use of a vector potential in reversed flow. We compare this behavior with analogous results for general pulsed-flow models. Some calculations using pulsed Beltrami waves are described.

ISSN:0309-1929    

DOI:10.1080/03091928908243461

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The magnetic fields of the Earth and other planets deviate in varying degrees from symmetry about the rotational axis. While, for example, the field of Saturn is highly symmetric, that of Uranus shows a striking asymmetry. With these observations in mind we investigate excitation conditions of axisymmetric and non-axisymmetric field modes in spherical mean-field dynamo models. In models of α2-type the marginal dynamo numbers for modes with different azimuthal dependences are close together if the α-effect is concentrated in a thin layer. Preference of non-axisymmetric modes over axisymmetric ones occurs if we include weak differential rotation, anisotropies of the α-effect or the γ-effect, the last one corresponding to a radial transport of magnetic flux. We discuss consequences of these results for planetary dynamos.

ISSN:0309-1929    

DOI:10.1080/03091928908243462

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The paper is based on an analysis by Boda and Sirá[nbreve] (1986) and Boďa (1988) of the instabilities of a horizontal layer of electrically conducting fluid which is rapidly rotating about a vertical axis, parallel to an applied vertical temperature gradient, and permeated by an azimuthal magnetic field that linearly increases with the distance from the axis. In the present configuration, a stably stratified sublayer is also included. This configuration is analysed using mean-field magnetohydrodynamics. The motions and magnetic fields due to the instabilities are considered as fluctuations. The mean electromotive force resulting from these fluctuations is computed, and its dependence on the magnetic field and the width of the unstably stratified sublayer is determined. The results are discussed in the context of the processes in the Earth's liquid core that are responsible for the main geomagnetic field.

ISSN:0309-1929    

DOI:10.1080/03091928908243463

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The paper deals with a spherical mean-field dynamo model of α2-type in which the back-reaction of the magnetic field on the fluid motion is taken into account by a dependence of the α-coefficient on either the total magnetic energy or the local magnetic energy density. Results of some experiments are presented which have been carried out with a numerical code that follows the evolution of the magnetic field. Particular attention is paid to steady fields and their stability. It is stressed that the results of stability analyses restricted to axisymmetric perturbations crucially differ from those that also include non-axisymmetric perturbations.

ISSN:0309-1929    

DOI:10.1080/03091928908243464

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Examination of the annual mean values of the geomagnetic elements from the world net of magnetic observatories shows that jerks took place in 1937, 1947, 1958, 1969. Eleven year smoothing and straight line approximations of first derivatives were used to analyse the magnetic components. To determine the ability of this technique in deciding whether the secular acceleration is constant between jerks epochs, spherical harmonic analysis of these components were performed. It is shown that the mean square field of a jerk assumes quite reasonable magnitudes for all jerks epochs. This point is illustrated by examples of contour maps of the fields of jerks, which show a number of foci in regions where there are a sufficient number of magnetic observatories. It is concluded that geomagnetic field dynamics may be assumed to be a series of quasi stable states each lasting a characteristic time of a few decades.

ISSN:0309-1929    

DOI:10.1080/03091928908243465

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Finite amplitude solutions for magnetohydrodynamic dynamos driven by convection in rotating spherical fluid shells with a radius ratio of ηequals; 0.4 are obtained numerically by the Galerkin method. Solutions which are twice periodic in the azimuth (casemequals; 2) are emphasized, but a few cases with higher azimuthal wavenumber have also been considered. An electrically insulating space outside the fluid shell has been assumed. A comparison of the dynamo solutions of both, dipolar and quadrupolar, symmetries with the corresponding non-magnetic solutions shows a strong increase of the amplitude of convection owing to the release of the rotational constraint by the Lorentz force. In some cases at low Taylor number the amplitude of convection is decreased, however, owing to the competition of the magnetic degree of freedom for the same energy source. The strength of differential rotation is usually reduced by the Lorentz force, especially in the case of quadrupolar dynamos which differ in this respect from dipolar dynamos for topological reasons. Some preliminary results on the stability of the steady dynamo solutions are also presented.

ISSN:0309-1929    

DOI:10.1080/03091928908243466

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

It is shown that the solutions of the linear (kinematic) geodynamo problem form a complete set of normalized eigenfunctions. Using an expansion of the solution of the nonlinear (dynamo) problem in a series of these eigenfunctions, the dynamo equations can be transformed into a finite system of ordinary differential equations.

ISSN:0309-1929    

DOI:10.1080/03091928908243467

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The stability of nonlinear mean-field dynamo models in spherical geometry has been investigated numerically. Assuming axisymmetry and incompressibility we find stable stationary solutions of both even and odd parity over a range of four decades in the Taylor number. Furthermore, we extend studies on solutions with “mixed parity”, which have been found previously for an αω-dynamo model, neglecting here, however, the explicit feedback on the mean motions. Plots of trajectories in phase space and Poincaré maps, showing intersections of the trajectories with certain hyperplanes in phase space, reveal that the solution lies on a torus for some of these models.

ISSN:0309-1929    

DOI:10.1080/03091928908243468

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor