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1.
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   

2.

A formal theory is presented for the balanced evolution of a small-amplitude, small-scale wave field in the presence of an axisymmetric vortex initially in gradient-wind balance and the accompanying changes induced in the vortex by the azimuthally averaged wave fluxes. The theory is a multi-parameter, asymptotic perturbation expansion for the conservative, rotating, f-plane, shallow-water equations. It extends previous work on Rossby-wave dynamics in vortices and more generally provides a new perspective on wave/mean-flow interaction in finite Rossby-number regimes. Some illustrative solutions are presented for a perturbed vortex undergoing axisymmetrization.  相似文献   

3.
Abstract

The equilibrium structure of an axisymmetric magnetic flux tube confined by an external pressure pe(Z) that varies along the length of the tube is studie. In the past, most work has concentrated on slender flux tubes, where the effects of transverse structure and radial fields are neglected. Here the aim is to explore the properties of thick tubes, in order to see to what extent the slender tube theory is valid. The main results are:  相似文献   

4.
Abstract

A new numerical approach is introduced which allows investigation into the conditions for dynamogeneration of axisymmetric and non-axisymmetric large-scale magnetic field modes in galaxy models which are defined by axisymmetric distributions of the α-parameter, the angular velocity and the electrical conductivity. The velocity field is assumed to be localized, however, the common assumption of a sharp boundary of the conducting region is dropped.

The possible anisotropy of the α-tensor is taken into account. The critical dynamo numbers (excitation conditions) for different modes are obtained by a direct method. The required steady states are attained by the use of an artificial non-linearity.

Initial test calculations demonstrate the efficacy of this new concept.  相似文献   

5.
Abstract

The purpose of this note is two-fold: to draw attention to a perplexing difficulty connected with topographic core-mantle coupling, and to suggest tentatively an explanation. The difficulty is an apparent conflict between the most comprehensive theory of the coupling so far attempted (Anufriev and Braginsky, 1975a, b, 1977a, b) and recent explicit calculations based on magnetic and seismic information (Speith et al., 1986). It is argued that asymmetric deviations from Anufriev and Braginsky's basically axisymmetric model of the underlying core flow are capable of resolving the difficulty.  相似文献   

6.
Abstract

The transition between axisymmetric and non-axisymmetric régimes of flow in a rotating annulus of liquid subject to horizontal temperature gradient is known from previous experimental studies to depend largely on two dimensionless parameters. These are Θ, which is proportional to the impressed density contrast Δρ and inversely proportional to the square of the angular speed of rotation ω, and  (Taylor number), which is proportional to ω2 /v2 where v is the coefficient of kinematic viscosity. At moderate values of , around 107, the critical value of Θ above which axisymmetric flow is found to OCCUT and below which non-axisymmetric fully-developed baroclinic waves (sloping convection) occur, is fairly insensitive to . Though sharp, the transition exhibits marked hysteresis when the upper surface of the liquid is free (but not when the upper surface is in contact with a rigid lid), and it is argued on the basis of the experimental evidence supported by various results of baroclinic instability theory that both the sharpness of the transition and the hysteresis phenomenon are consequences of the combined effects of potential vorticity gradients and viscosity on the process of sloping convection.

We also present some new experiments on fully-developed baroclinic waves, conducted in a large rotating annulus using liquids of very low viscosity (di-ethyl ether), thus attaining values of  as high as 109 to 1010. The transition from axisymmetric to non-axisymmetric flow is found to lose its sharpness at such high values of , and it is argued that this occurs because viscosity is no longer able to inhibit instabilities at wavelengths less than the so-called ‘Eady short-wave cut-off’, which owe their existence to potential vorticity gradients in the main body of the fluid.  相似文献   

7.
Abstract

Methods of estimating the strength and direction of galactic magnetic fields from radio polarization measurements are reviewed. Particular attention is paid to the analysis of the Faraday rotation in order to derive the large scale magnetic field structure. Ways in which an axisymmetric spiral field structure can be observationally distinguished from a bisymmetric spiral structure are described, as are the ways in which field symmetric with respect to the galactic plane can be distinguished from those that are antisymmetric.  相似文献   

8.
Abstract

The “viscous overturning” mechanism, described in its simplest form by the linearized instability theory of the previous paper, is discussed in relation to certain numerical solutions recently obtained by G. P. Williams for steady thermally driven axisymmetric convective flow of water (Prandtl number = 7) in a rotating annulus differentially heated in the horizontal, in the “upper symmetric regime” parameter range. Viscous overturning plays an important and clearly identifiable role in the flows A3B, A4 and A5, which have free‐slip side walls and top surface, and a less clearcut role in A3 and B2, for which only the top surface is free. The discussion leads to various predictions about annulus flows not yet studied in detail.  相似文献   

9.
Abstract

We present trial calculations for a simple nonlinear ‘‘thick disk'’ galaxy dynamo. The nonlinearity is a simple α-quenching. Our strictly axisymmetric solution demonstrates the possibility of a nonlinear interaction between modes of opposite parity. We suggest that a three dimensional model might exhibit a similar persistent interaction between axisymmetric and non-axisymmetric modes.  相似文献   

10.
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   

11.
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   

12.
ABSTRACT

It 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   

13.
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   

14.
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   

15.
Abstract

This paper presents the first attempt to examine the stability of a poloidal magnetic field in a rapidly rotating spherical shell of electrically conducting fluid. We find that a steady axisymmetric poloidal magnetic field loses its stability to a non-axisymmetric perturbation when the Elsasser number A based on the maximum strength of the field exceeds a value about 20. Comparing this with observed fields, we find that, for any reasonable estimates of the appropriate parameters in planetary interiors, our theory predicts that all planetary poloidal fields are stable, with the possible exception of Jupiter. The present study therefore provides strong support for the physical relevance of magnetic stability analysis to planetary dynamos. We find that the fluid motions driven by magnetic instabilities are characterized by a nearly two-dimensional columnar structure attempting to satisfy the Proudman-Taylor theorm. This suggests that the most rapidly growing perturbation arranges itself in such a way that the geostrophic condition is satisfied to leading order. A particularly interesting feature is that, for the most unstable mode, contours of the non-axisymmetric azimuthal flow are closely aligned with the basic axisymmetric poloidal magnetic field lines. As a result, the amplitude of the azimuthal component of the instability is smaller than or comparable with that of the poloidal component, in contrast with the instabilities generated by toroidal decay modes (Zhang and Fearn, 1994). It is shown, by examining the same system with and without fluid inertia, that fluid inertia plays a secondary role when the magnetic Taylor number Tm ? 105. We find that the direction of propagation of hydromagnetic waves driven by the instability is influenced strongly by the size of the inner core.  相似文献   

16.
Abstract

The linear stability analysis of Hathaway, Gilman and Toomre (1979) (hereafter referred to as Paper I) is repeated for Boussinesq fluids with viscous and thermal diffusion. As in Paper I the fluid is confined between plane parallel boundaries and the rotation vector is oblique to gravity. This tilted rotation vector introduces a preference for roll-like disturbances whose axes are oriented north-south; the preference is particularly strong in the equatorial region. The presence of a latitudinal temperature gradient produces a thermal wind shear which favors axisymmetric convective rolls if the gradient exceeds some critical value. For vanishingly small diffusivities the value of this transition temperature gradient approaches the inviscid value found in Paper I. For larger diffusivities larger gradients are required particularly in the high latitudes. These results are largely independent of the Prandtl number. Diffusion tends to stabilize the large wavenumber rolls with the result that a unique wavenumber can be found at which the growth rate is maximized. These preferred rolls have widths comparable to the depth of the layer and tend to be broader near the equator. The axisymmetric rolls are similar in many respects to the cloud bands on Jupiter provided they extend to a depth of about 15,000 km.  相似文献   

17.
Observational evidence suggests that black smoker chimneys are formed by the precipitation of anhydrite from seawater producing a solid framework which is replaced successively by iron, zinc and copper sulfides. We have demonstrated the feasibility of this process using a laboratory model in which KNO3 is first crystallized from a warm, nearly saturated solution round an inflowing plume of cold K2CO3. The chimney grows in length at a nearly constant rate and, at the same time, it thickens as heat conduction causes further crystallization. The dynamic replacement process has been modelled separately, with CuSO4 passed through a previously formed chimney of KNO3 and flowing out through the porous walls when the flow rate, and hence the pressure difference, is increased. The formation of chimneys at a line or slit source has also been investigated in the laboratory. It has been shown that, in this case, the slit is quickly blocked off by crystallization over most of its length and that the growth is concentrated at just a few points to form a small number of nearly axisymmetric chimneys.A theory has been developed which predicts both the diameter of the outlet vent and the sign of the pressure difference between the inside and the outside of an axisymmetric chimney of constant internal diameter for a specified flow rate and density difference. It suggests that changes in flow rate or in the internal diameter of the chimney can cause fluid to flow in or out through the porous wall, leading to changes in the position of mineral stability fields within the evolving chimney. The theory has been extended to describe the pressure distribution in tapering interior conduits and it leads to the conclusion that the direction of flow through a porous chimney can reverse along its length.  相似文献   

18.
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   

19.
Abstract

Using a contour dynamical algorithm, we have found rotating tripolar V-state solutions for the inviscid Euler equations in two-dimensions. We have studied their geometry as a function of their physical parameters. Their stability was investigated with the aid of contour surgery, and most of the states were found to be stable. Under finite-amplitude perturbations, tripoles are shown to either fission into two asymmetric dipoles or to evolve into a shielded axisymmetric vortex, demonstrating the existence of two new ‘‘reversible transitions'’ between topologically distinct coherent vortex structures. These dynamical results are confirmed by pseudo-spectral simulations, with which we also show how continuous tripolar long-lived coherent vortex structures can be generated in a variety of ways.  相似文献   

20.
Abstract

The south-easterly surface flow down the slopes of Antarctica induces a transfer of westerly angular momentum to the atmosphere, which must be removed from the Antarctic domain by atmospheric transports. It is suggested that synoptic eddies protruding from the northern baroclinic zone into the polar regions are modified by the topography such that they are able to perform these meridional transports. A simple linear two-layer model of the axisymmetric circulation of Antarctica is presented where the eddy effects are incorporated via a K-ansatz. It is shown that qualitatively realistic mean flow patterns can be obtained with this model. The limitations of this approach are exposed.  相似文献   

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