共查询到20条相似文献，搜索用时 31 毫秒
1.
Abstract An idealised α2ω-dynamo is considered in which the α-effect is prescribed. The additional ω-effect results from a geostrophic motion whose magnitude is determined indirectly by the Lorentz forces and Ekman suction at the boundary. As the strength of the α-effect is increased, a critical value α? c is reached at which dynamo activity sets in; α? c is determined by the solution of the kinematic α2-dynamo problem. In the neighbourhood of the critical value of α? the magnetic field is weak of order E 1/4(μηρω)½ due to the control of Ekman suction; E(?1) is the Ekman number. At certain values of α?, viscosity independent solutions are found satisfying Taylor's constraint. They are identified by the bifurcation of a nonlinear eigenvalue problem. Dimensional arguments indicate that following this second bifurcation the magnetic field is strong of order (μηρω)½. The nature of the transition between the kinematic linear theory and the Taylor state is investigated for various distributions of the α-effect. The character of the transition is found to be strongly model dependent. 相似文献
2.
A. P. Anufriev 《地球物理与天体物理流体动力学》2013,107(1-4):269-273
Abstract Latitude behavior of the boundary α-effect based on reflection of hydromagnetic waves from the Core-Mantle Boundary (CMB) studied earlier by Anufriev (1991), is discussed. Its form given in Figure 2 is in good agreement with that used in model-Z of Braginsky. We want to emphasize the following main features of our α-effect which resemble those of Braginsky: concentration near the boundary, sign-changing of α in the layer and geometrical behavior. The last includes the vanishing of α near the poles and the equator which is characteristic for Braginsky's α-effect. It is also shown that for Magnetic Reynolds Number of order 100 the amplitude of the α-effect and the thickness of the α-layer is of the order of those used in model-Z. 相似文献
3.
I. Cupal 《地球物理与天体物理流体动力学》2013,107(1-4):165-180
Abstract An attempt has been made to include the axially asymmetric velocities into the calculation of Braginsky's Z-model of the nearly symmetric hydromagnetic dynamo. In this axisymmetric non-linear model dominated by Lorentz and Coriolis forces and maintained by a specified convection, the α-effect is prescribed. An example is shown of the axially asymmetric Archimedean buoyancy, which can imply an arbitrary alpha effect in the model with viscous core-mantle coupling. The formalisms of Tough and Roberts (1968) is also discussed and a modified α-effect in the Z-model is suggested. 相似文献
4.
Vladislav Zheligovsky 《地球物理与天体物理流体动力学》2013,107(5):489-540
We consider stability of regimes of hydromagnetic thermal convection in a rotating horizontal layer with free electrically-conducting boundaries, to perturbations involving large spatial and temporal scales. Equations governing the evolution of weakly nonlinear mean perturbations are derived under the assumption that the α-effect is insignificant in the leading-order (e.g. due to a symmetry of the system). The mean-field equations generalise the standard equations of hydromagnetic convection: New terms emerge – a second-order linear operator representing the combined eddy diffusivity and quadratic terms associated with the eddy advection. If the perturbed CHM regime is nonsteady and insignificance of the α-effect in the system does not rely on the presence of a spatial symmetry, the combined eddy diffusivity operator also involves a nonlocal pseudodifferential operator. If the perturbed CHM state is almost symmetric, α-effect terms appear in the mean-field equations as well. Near a point of a symmetry-breaking bifurcation, cubic nonlinearity emerges in the equations. All the new terms are in general anisotropic. A method for evaluation of their coefficients is presented; it requires solution of a significantly smaller number of auxiliary problems than in a straightforward approach. 相似文献
5.
Abstract It is shown that, for general homogeneous turbulence, the anti-symmetric part of the spectrum tensor can be expressed in terms of a single scalar function H(k,ω) (the helicity spectrum function). Under the first-order smoothing approximation, the coefficients α ij β ijk in the expansion of the mean electromotive force in terms of the mean magnetic field are determined; α ij is a weighted integral of H(k,ω), and β ijk contains a part β(a)ijk which is likewise a weighted integral of H(k, ω). When the turbulence is axisymmetric, β(a)ijk contains Rädler's (1969a) “Ω ∧ J-effect”. It is shown that when the turbulence is statistically symmetric about a plane perpendicular to the axis of symmetry, then βij = O but the Rädler effect is non-zero. Explicit expressions for αij and βijk are given when the velocity field is generated by random forcing in a rotating medium. Finally, it is shown by means of a local analysis that the Rädler effect, in conjunction with uniform mean shear, can give rise to non-oscillatory dynamo action, and it is argued that this effect may be significant in the well-mixed interior of a stellar convection zone, where by symmetry the α-effect may be weak. 相似文献
6.
N. A. Silant'ev 《地球物理与天体物理流体动力学》2013,107(1-2):99-125
Abstract First the exact numerical solutions of DIA system of equations describing the transportation of magnetic field in an infinite medium are presented. It is assumed that the turbulence is stationary, homogeneous, isotropic and incompressible. The spectra of turbulence of δ-type and Kolmogorov's type were used. The steady state values of magnetic field diffusivity DT and the α-effect coefficient α T were calculated for various values of space-scale and lifetimes of these spectra and the spectra of helicity. Also investigated is the dependence of DT and α T on the degree of helicity. The corrections to the α T -coefficient due to the contribution of four-order velocity correlators are given. The results are compared with those due to the self-consistent technique. 相似文献
7.
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
8.
The dynamics of the Earth's core are dominated by a balance between Lorentz and Coriolis forces. Previous studies of possible (magnetostrophic) hydromagnetic instabilities in this regime have been confined to geophysically unrealistic flows and fields. In recent papers we have treated rather general fields and flows in a spherical geometry and in a computationally simple plane-layer model. These studies have highlighted the importance of differential rotation in determining the spatial structure of the instability. Here we have proceeded to use these results to construct a self-consistent dynamo model of the geomagnetic field. An iterative procedure is employed in which an α-effect is calculated from the form of the instability and is then used in a mean field dynamo model. The mean zonal field calculated there is then input back into the hydromagnetic stability problem and a new α-effect calculated. The whole procedure is repeated until the input and output zonal fields are the same to some tolerance. 相似文献
9.
10.
11.
Abstract In a previous paper, Bassom et al. (Proc. R. Soc. Lond. A, 455, 1443–1481, 1999) (BKS) investigated finite amplitude αΩ-dynamo wave trains in a thin turbulent, differentially rotating convective stellar shell; nonlinearity arose from α-quenching. There asymptotic solutions were developed based upon the small aspect ratio ε of the shell. Specifically, as a consequence of a prescribed latitudinally dependent α-effect and zonal shear flow, the wave trains have smooth amplitude modulation but are terminated abruptly across a front at some high latitude θF. Generally, the linear WKB-solution ahead of the front is characterised by the vanishing of the complex group velocity at a nearby point θf; this is essentially the Dee–Langer criterion, which determines both the wave frequency and front location. Recently, Griffiths et al. (Geophys. Astrophys. Fluid Dynam. 94, 85–133, 2001) (GBSK) obtained solutions to the α2Ω-extension of the model by application of the Dee—Langer criterion. Its justification depends on the linear solution in a narrow layer ahead of the front on the short O(θf—θF) length scale; here conventional WKB-theory, used to describe the solution elsewhere, is inadequate because of mode coalescence. This becomes a highly sensitive issue, when considering the transition from the linear solution, which occurs when the dynamo number D takes its critical value D c corresponding to the onset of kinematic dynamo action, to the fully nonlinear solutions, for which the Dee—Langer criterion pertains. In this paper we investigate the nature of the narrow layer for α2Ω-dynamos in the limit of relatively small but finite α-effect Reynolds numbers R α, explicitly ε½ ? R 2 α ? 1. Though there is a multiplicity of solutions, our results show that the space occupied by the corresponding wave train is generally maximised by a solution with θf—θF small; such solutions are preferred as evinced by numerical simulations. This feature justifies the application by GBSK of the Dee—Langer criterion for all D down to the minimum D min that the condition admits. Significantly, the frontal solutions are subcritical in the sense that |D min| ≤ |D c|; equality occurs as the α-effect Reynolds number tends to zero. We demonstrate that the critical linear solution is not connected by any parameter track to the preferred nonlinear solution associated with D min. By implication, a complicated bifurcation sequence is required to make the connection between the linear and nonlinear states. This feature is in stark contrast to the corresponding results for αΩ-dynamos obtained by BKS valid in the limit R 2 α ? ε½, which, though exhibiting a weak subcriticality, showed that the connection follows a clearly identifiable nonbifurcating track. 相似文献
12.
Jim Stone 《地球物理与天体物理流体动力学》2013,107(6):507-508
The velocity, pressure, perturbation magnetic field, helicity and electromotive force driven by an isolated buoyant parcel in an unbounded, rapidly rotating, electrically conducting fluid in the limit of small Elsasser number and very small Ekman number are calculated, visualized and analyzed. On the scale of the parcel, the solution is identical to that obtained in the limit of small Ekman number and zero Elsasser number. On the scale of the Taylor-column, it is elongated in the direction of the applied magnetic field and compressed in the direction perpendicular to it. The α-effect calculated by averaging the electromotive force on planes normal to rotation is strongly anisotropic: near the parcel and in the inner part of the Taylor-column it is strongest when the applied magnetic field is perpendicular to rotation and gravity; in the outer part of the Taylor-column it is strongest when the applied magnetic field is in the same plane as rotation and gravity. 相似文献
13.
Phillip Hignett 《地球物理与天体物理流体动力学》2013,107(3-4):293-299
Abstract Some new measurements are presented of the axisymmetric heat transport in a differentially heated rotating fluid annulus. Both rigid and free upper surface cases are studied, for Prandtl numbers of 7 and 45, from low to high rotation rates. The rigid lid case is extended to high rotation rates by suppressing the baroclinic waves, that would normally develop at some intermediate rotation rate, with the use of sloping endwalls. A parameter P is defined as the square of the ratio of the (non-rotating) thermal sidewall layer thickness to the Ekman layer thickness. For small P the heat transport remains unaffected by the rotation, but as P increases to order unity the Ekman layer becomes thin enough to inhibit the radial mass transport, and hence the heat flux. No explicit Prandtl number dependence is observed. Also this scaling allows the identification of the region in which the azimuthal velocity reaches its maximum. Direct comparisons are drawn with previous experimental and numerical results, which show what can be interpreted as an inhibiting effect of increasing curvature on the heat transport. 相似文献
14.
A. Tilgner 《地球物理与天体物理流体动力学》2013,107(3):225-234
In geodynamo simulations which simulate the generation of an axial dipolar magnetic field, the generation mechanism appears to be adequately described as an α2-dynamo with an anisotropic α-effect. The anisotropy in the α-effect favors an equatorial dipole field, however, which calls into question the interpretation in terms of an α2-dynamo. It is shown in this article with kinematic dynamo calculations and exemplary velocity fields with an anisotropic α-effect that both types of dipolar magnetic field can be generated. Two examples of working dynamos in a sphere with flows with zero α-effect are also provided. 相似文献
15.
Abstract Inertial waves are excited in a fluid contained in a slightly tilted rotating cylindrical cavity while the fluid is spinning up from rest. The surface of the fluid is free. Since the perturbation frequency is equal to the rotation speed resonance occurs at a critical height to radius aspect ratio of the fluid. Detailed study of a particular inertial wave shows that in solid body rotation this “eigenratio” agrees with predictions from linear inviscid theory to within 0.5%. Measured time dependence of the eigenratio during spin-up from rest is a function of the tilt amplitude and agrees favorably with predictions from a numerical study. Mean flow associated with the inertial wave becomes unstable during spin-up and in the steady state. A boundary for the unstable region is found experimentally. 相似文献
16.
J. E. Hart 《地球物理与天体物理流体动力学》2013,107(1):181-209
AbstractExperimental and theoretical results are presented for a simple system which exhibits baroclinic instability. We consider the motion of two immiscible fluids with densities ρ 1 and ρ 2 contained in a cylinder rotating with angular frequency ω. The motion is driven by a contact lid rotating with frequency ω + ω. In this paper ω, ω, 2(ρ 2 – ρ 1)/(ρ 2 + ρ 1), and the geometry are such that the interface does not intersect the “ground” (e.g. an almost horizontal boundary). The motions are described by two-layer quasi-geostrophic equations which are identical, except perhaps for the presence of interfacial friction and tension, with those used in meteorology and oceanography. For small enough internal Froude number F = 4ω2 L 2/(g(Δρ/ρ)H) or small enough Rossby number ? = ω/2ω the flow is steady and axisymmetric, the velocity field in each layer being determined primarily by frictional effects in top, bottom, and interfacial Ekman layers. For certain (F, ?) the flow becomes non-axisymmetric. The transition points for the case where the basic potential vorticity gradient is due to interface slope alone have been carefully measured and are in very good agreement with a linear instability theory which neglects sidewall effects. Some preliminary observations of supercritical motion, which include repeatable amplitude and wavenumber vacillation, are reported. 相似文献
17.
A. E. Gledzer E. B. Gledzer A. A. Khapaev O. G. Chkhetiani S. L. Shalimov 《Izvestiya Physics of the Solid Earth》2018,54(4):574-586
The results of the laboratory and numerical experiments in circular rotating trays with thin layers of a conductive fluid under the MHD generation of small-scale velocity fields are presented. The configurations of constant magnets for MHD generation were determined based on the numerical calculations with shallow water equations. Both the laboratory and numerical experiments with rotating trays demonstrate the emergence of nonaxisymmetric structures and large-scale near-circular vortices caused by the energy transfer from the system of the externally generated small-scale vortices to the large-scale velocity fields under the action of the Coriolis force. The near-circular vortex has areas with differential rotation when the angular velocity of rotation decreases with the radius. The single large-scale vortices and wide jet flows arise in the regimes of subrotation and superrotation relative to the external rotation depending on its angular velocity. The emergence of the flow structures with the azimuthal wave number m = 2 is demonstrated, and their probable relation to the anomalies of the geomagnetic field observed on the Earth’s surface is considered. 相似文献
18.
Alice Courvoisier 《地球物理与天体物理流体动力学》2013,107(2):217-243
We look at the large-scale dynamo properties of spatially periodic, time dependent, helical 2D flows of the form u(x, t)?=?(? y ?ψ?(x, y, t), ?? x ?ψ?(x, y, t), ?ψ (x, y, t). These flows act as kinematic fast dynamos and are able to generate a mean magnetic field uniform and constant in the xy-plane but whose direction varies periodically along z with wavenumber k. Using Mean Field Electrodynamics, the generation mechanism can be understood in terms of a k-dependent α-effect, which depends on the magnetic Reynolds number, R m . We calculate this effect for different motions and investigate how its limit as k?→?0 depends on R m and on the properties of the flows such as their spatial structure or correlation time. This work generalises earlier studies based on 2D steady flows to motions with time dependence. 相似文献
19.
P. M. Serebrianaya 《地球物理与天体物理流体动力学》2013,107(1-4):141-164
Abstract This paper is concerned with a three-dimensional spherical model of a stationary dynamo that consists of a convective layer with a simple poloidal flow of the S2c 2 kind between a rotating inner body core and solid outer shell. The rotation of the inner core and the outer shell means that there are regions of concentrated shear or differential rotation at the convective layer boundaries. The induction equation for the inside of the convective layer was solved numerically by the Bullard-Gellman method, the eigenvalue of the problem being the magnetic Reynolds number of the poloidal flow (R M2) and it was assumed that the magnetic Reynolds number of the core (R M1) and of the shell (R M3) were prescribed parameters. Hence R M2 was studied as a function of R M1 and R M3, along with the orientation of the rotation axis, the radial dependence of the poloidal velocity and the relative thickness of the layers for the three different situations, (i) the core alone rotating, (ii) the shell alone rotating and (iii) the core and the shell rotating together. In all three cases it was found that, at definite orientations of the rotation axis, there is a good convergence of both the eigenvalues and the eigenfunctions of the problem as the number of spherical harmonics used to represent the problem increases. For R M1 =R M3= 103, corresponding to the westward drift velocity and the parameters of the Earth's core, the critical values of R M2 are found to be three orders of magnitude lower than R M1, R M3 so that the poloidal flow velocity sufficient for maintaining the dynamo process is 10-20 m/yr. With only the core or the shell rotating, the velocity field generally differs little from the axially symmetric case. However, for R M2 (or R M3) lying in the range 102 to 105, the self-excitation condition is found to be of the form R M2˙R ½ M1=constant (or R M2˙R½ M3=constant) and the solution does not possess the properties of the Braginsky near-axisymmetric dynamo. We should expect this, in particular, in the Braginsky limit R M2˙R?½; M1=constant. An analysis of known three-dimensional dynamo models indicates the importance of the absence of mirror symmetry planes for the efficient generation of magnetic fields. 相似文献
20.
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