ISSN:0309-1929    

DOI:10.1080/03091929208201833

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

The α2-dynamo of Hollerbach and Ierley (1991) is converted into an αω-dynamo, and the analysis of Barenghi and Jones (1991) is extended. Only one choice of α and ω is considered in detail, for both negative and positive dynamo numbers. The solutions in the viscously limited regime are qualitatively distinct, with negativeDsolutions oscillating about a zero mean, and positiveDsolutions oscillating about a non-zero mean. The existence of nonlinear eigenvaluesDxis demonstrated, beyond which the solutions are no longer viscously limited. The subsequent evolution would appear to be independent of the viscosity in some average sense, but there is no evidence of a true Taylor state.

ISSN:0309-1929    

DOI:10.1080/03091929208201834

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

The magnetic field of a rapidly rotating α2dynamo is computed in a spherical shell as a function of Reynolds and Ekman numbers. It is found that at high enough Reynolds number a Taylor state is reached, after which the solution becomes inviscid. This result confirms the recent work of Hollerbach and Ierley (1991) in a full sphere.

ISSN:0309-1929    

DOI:10.1080/03091929208201835

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

Nonlinear αω dynamo models in a duct geometry are considered. The rapid rotation approximation, in which inertial terms are neglected and viscosity is only significant in boundary layers, is used. The nonlinearities that arise in the model are the magnetically driven geostrophic flow and meridional circulation. The numerical method used is a two-dimensional, time-stepping spectral code.

ISSN:0309-1929    

DOI:10.1080/03091929208201836

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

The amplitudes of the magnetic field generated by various α2-dynamo models are investigated for the case when the magnetic Reynolds number,R, slightly exceeds the critical value,R(0), at which dynamo action is marginally possible. The basic assumption is that the α-effect is modified by the presence of the magnetic field by an amount proportional to the local magnetic energy density, according to the quenching law α = α0− α1|B|2, whereBis the magnetic field and α0and α1are positive constants. Solutions were obtained by expanding the field in powers of the amplitude, a, ofB, and by solving the resulting perturbation equations up to third order in a with the help of the adjoint kinematic dynamo system. An expression for the growth rate, γ1, of an infinitesimal disturbance whenR — R(0)is small was obtained, and the amplitude, a(0), of the final (stable) state was derived. Numerical integrations were performed for five models originally due to Roberts (1972) as well as for a model studied by Rädler and Wiedemann (1989). In all cases, the eigenvalues, the eigenfunctions, and the parameters needed to determine the final steady state (i.e., γ1and the Landau constant) show satisfactory numerical evidence of convergence. It was found that the bifurcation is supercritical for all six models. The critical Reynolds number for the dipole family of solutions is quite close to that of the quadrupole family of solutions in each case, as are the final steady-state amplitudes. The six models behave differently at finite amplitudes, and in particular there appears to be no correlation between the relative amplitudes of the steady dipole and quadrupole solutions and the relative sizes ofR(0)for the two families.

ISSN:0309-1929    

DOI:10.1080/03091929208201837

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

The main subject of the paper is to show how the shape and thickness of an α-layer and the amplitude of the α-effect influence the solution of model Z, especially the magnetic field energy (MFE). Solution of model Z with different input parameters allows us to conclude that the larger the thickness of the α-layer, the greater the ratio of the MFE of the meridional to the MFE of the azimuthal field and, therefore, the greater the efficiency of the α-effect, although the appropriate value of the amplitude of the α-effect is more difficult to find. The MFE tends to oscillate for a sufficiently thick α-layer if the amplitude of the α-effect is changed, but the oscillations are suppressed and MFE is again stabilized. If the thickness of the α-layer does not vary, the MFE of the azimuthal field relative to the MFE of the meridional field decreases with increasing amplitude of the α-effect in certain narrow limits. The geostrophic shear does not change its character, and its maximum follows the maximum of α-effect in the layer.

ISSN:0309-1929    

DOI:10.1080/03091929208201838

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

The problem of numerically simulating a rapidly rotating, strong field dynamically consistent MHD dynamo is considered, and the advantages of using the magnetostrophic approximation in lieu of the momentum equation are discussed strictly in terms of lengthening the allowable time step for a given numerical method. One possible magnetostrophic state, the Taylor state, is investigated, and both the Taylor constraint and the Taylor algorithm are extended to include a family of volumes of revolution not previously studied. The Taylor algorithm is here found to be stable in the sense that it gives a good approximation to a solution of the full system as long as the equation governing the geostrophic velocity is well-posed. Conditions under which this equation becomes ill-posed and the Taylor state ends are discussed.

ISSN:0309-1929    

DOI:10.1080/03091929208201839

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

We investigate solvability conditions for the magnetostrophic equation for dynamo models which are neither axisymmetric nor contained within an insulating sphere. Effects of topography and mantle conductivity are discussed. Simplifications that apply for axisymmetric fields contained in a perfectly insulating mantle no longer apply and we conclude that the standard manipulation of the Taylor integral is no longer helpful; it is best used in its original form ∫J×Bdzd. Electromagnetic and topographic core-mantle coupling are fundamentally different to viscous coupling. For the latter, the magnetostrophic equation always has a solution (due to the role of Ekman suction). For the former (in the absence of viscous coupling), a solution requires that Taylor's condition be satisfied. For the case of electromagnetic coupling, we derive the appropriate magnetic boundary conditions for various models of iower mantle conductivity. Finally, we derive the solvability condition (analogous to Taylor's condition) appropriate for a core-mantle boundary with topography.

ISSN:0309-1929    

DOI:10.1080/03091929208201840

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

This paper analyzes the linear stability of a rapidly-rotating, stratified sheet pinch in a gravitational field, g, perpendicular to the sheet. The sheet pinch is a layer (O ⩽ z ⩽ d) of inviscid, Boussinesq fluid of electrical conductivity σ, magnetic permeability μ, and almost uniform densityρo; z is height. The prevailing magnetic field.Bo(z), is horizontal at each z level, but varies in direction with z. The angular velocity,Ω, is vertical and large (Ω ≫ VA/d, where VA= B0√(μρ0) is the Alfvén velocity). The Elsasser number, Λ = σB20/2Ωρ0, measures σ. A (modified) Rayleigh number, R = gβd2/ρ0V2A, measures the buoyancy force, where β is the imposed density gradient, antiparallel tog. A Prandtl number, PK= μσK, measures the diffusivity, k, of density differences.

ISSN:0309-1929    

DOI:10.1080/03091929208201841

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

ISSN:0309-1929    

DOI:10.1080/03091929208201842

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor