INTRODUCTION

The influence of varying conductivity on the dynamo process has been investigated for example for galaxies (Donner & Brandenburg 1990) and accretion disks (Stepinski & Levy 1991) and found to be negligible there. Jeanloz's (1990) interpretation of the D′′ layer as a laterally inhomogeneous distribution of conducting and insulating alloys, resulting from chemical reactions at the core-mantle boundary and the percolation of iron into the mantle, has motivated us to consider the possibility of a dynamo induced by varying conductivity on the Earth's dynamo. Two questions arise in this context. Firstly, one may ask how a lower mantle with laterally varying conductivity will affect the extrapolation of magnetic fields from the Earth surface to the core. Poirier & le Mouel (1992) have investigated this question in detail and found the effect to be negligible. Jeanloz's (1990) view of pinned fieldlines is too dramatic.

INTRODUCTION

Very naturally, many of the investigations into astrophysical dynamo theory have been directed to explaining the Solar cycle: after all, this is the system for which the most detailed information, both spatial and temporal, is available. The large scale Solar magnetic field appears to be approximately axisymmetric and so it is appropriate to study strictly axisymmetric dynamos. More recently, evidence has accumulated that magnetic fields with a significant nonaxisymmetric component may be present in late type ‘active giant’ stars (see, e.g., the discussion in Moss et al. 1991a, and references therein), and also in one or two spiral galaxies, notably M81 (e.g. Krause et al. 1989; Sokoloff et al. 1992). Thus the conditions under which nonaxisymmetric fields can be excited in astrophysical systems are of current interest. Radler et al. (1990) and Moss et al. (1991a) have recently investigated nonlinear spherical mean field dynamo models in which stable nonaxisymmetric fields may be excited with suitably chosen distributions of alpha effect and differential rotation; see also Stix (1971). Rüdiger & Elstner (1992) considered models where the introduction of an anisotropy in the alpha tensor may have a similar effect; see also Rüdiger (1980).

INTRODUCTION

It is widely appreciated that magnetic fields can play an important role in accretion disk dynamics. Shakura & Sunyaev (1973), in their well known paper, pointed to magnetic fields as the source of a viscous couple necessary for the accretion to take place. Disk magnetic fields have also been invoked to explain spectra of compact X-ray sources, as a source of coronal heating, and as a source of wind production. In the context of the Solar nebula, which is widely assumed to represent a typical protoplanetary disk, the existence of a magnetic field is inferred from the residual magnetization of primitive meteorites, which are assumed to owe their magnetization to nebular magnetic fields. However, in a typical accretion disk, the timescale for ohmic dissipation is much smaller than the typical radial infall time, thus it is difficult to see how any magnetic field contained in the gas that falls onto the disk can persist long enough to be dynamically or otherwise important, unless it is regenerated by a dynamo cycle.

INTRODUCTION

Rotating fluid dynamics is of primary importance in the understanding of the origin of planetary magnetic fields which are generated by dynamo processes in the rotating fluid interiors of planets. There are two important but traditionally separate branches in the subject of rotating fluid dynamics: inertial oscillation and convection. Both have been extensively investigated. Inertial oscillation in rotating systems is governed by the Poincare equation; it was also shown by Malkus (1967) that the problem of hydromagnetic inertial oscillation can be changed to the Poincaré problem with a special form of the basic field. A classic introduction and most of the earlier research results concerning this problem can be found in Greenspan's monograph (1969). The important application to the dynamics of the Earth's fluid core was discussed by Aldridge & Lumb (1987).

INTRODUCTION

Starting with the paper of Parker (1955), one of the main purposes of scientists working in Solar physics was directed towards the understanding of the mechanisms governing the generation and the maintenance of the magnetic field that plays a central role in the Solar activity process. Many characteristic features, for example the well-known ‘butterfly’ diagram, are well described by kinematic dynamo theories. Great efforts are now directed towards the derivation of dynamo models that could agree with recent helioseismological data, and there is accumulating evidence that the seat of the dynamo is in the overshoot layer at the base of the convection zone (see for example, De Luca & Gilman 1991).

However, even the most sophisticated theories based mainly on the magnetic field are not able to explain topological aspects of Solar activity structures like active longitudes.

The screw dynamo is one of the simplest examples of a conducting fluid flow in which magnetic field can be self-excited provided the magnetic Reynolds number is sufficiently large (see, e.g., Roberts 1993). Such a flow can be encountered in some astrophysical objects and also in such technological devices as breeder reactors. For example, jet outflows in active galaxies and near young stars can be swirling. A flow of this type is used for modelling the dynamo effects in laboratory conditions (Gailitis 1993). The generation of magnetic fields by a laminar flow with helical streamlines was discussed by Lortz (1968), Ponomarenko (1973), Gailitis & Freiberg (1976), Gilbert (1988), Ruzmaikin et al. (1988) and other authors as an eigenvalue problem. Below we use the results of the asymptotic analysis of this problem for large Rm by Ruzmaikin et al.

We introduce an axisymmetric velocity field whose cylindrical polar components are (0, rω(r), v2(r)), with (r, φ, z) the cylindrical coordinates. We

consider smooth functions v2(r) and ω(r) vanishing as r → ∞. Both v2 (0) and ω(0) are assumed to be of order unity.

For Rm ≫ 1, an eigenmode of the screw dynamo represents a dynamo wave concentrated in a cylindrical shell of thickness ≃Rm−1/4 a certain radius r0.

INTRODUCTION

Stretching of line elements in fluids with or without conductivity is studied from various points of view. Firstly, simultaneous concentration of vortex and magnetic tubes is considered in section 2 by presenting an exact solution of the axisymmetric MHD equation for a viscous, incompressible, conducting fluid. This solution (Kambe 1985) tends to a stationary state that results from complete balance of convection, diffusion and stretching. Sections 3 and 4 are concerned with mathematical formulation based on Riemannian differential geometry, and global (mean) stretching of line elements is considered.

The general form of the Riemannian curvature tensor for any Lie group was derived by Arnold (1966), where explicit formulae for T2 (two-torus) were given. Explicit expressions for diffeomorphism curvatures on Tn (and even on any locally flat manifold) were described by Lukatskii (1981). Recently, Nakamura et al. (1992) considered the curvature form on T3 corresponding to three-dimensional motion of an ideal fluid with periodic boundary conditions in a cubic space. An immediate consequence is the property that the section curvature in the space of ABC diffeomorphisms is a negative constant for all the sections (Kambe et al. 1992).

INTRODUCTION

Chaotic dynamical systems can be grouped into two classes according to the characteristics of their behavior. One class is characterized by aperiodic modulations of already periodic signals while the other class is characterized by signals which exhibit apparently random switching between qualitatively different kinds of behavior. The latter behavior is called intermittency. Examples of intermittency are abundant in nature. They include intermittent bursts of turbulence in otherwise laminar pipe flow in fluid dynamics, sunspot activity in astrophysics, and stock market crashes in economics. A model of intermittency in terms of dynamical systems as well as a partial classification of some types of intermittency was given by Pomeau & Manneville (1980). In general, signals produced by this scenario are periodic oscillations interrupted from time to time by some aperiodic bursts of activity. Another model of intermittency, crisis-induced intermittency, was introduced by Grebogi, Ott, Romeiras & Yorke (1987). This intermittency involves a collision in phase- space of two chaotic attractors as some parameter is varied, and it is again characterized by random switching between different aperiodic oscillations.

ABSTRACT

We present infrared images and infrared spectroscopy of the suspected very young supernova remnant G25.5+0.2 first detected at radio wavelengths. The 2.2 μm image exhibits a similar nebular structure to that seen in the radio. Spectroscopic measurements at 2.17 μm show a Brackett gamma line that has the line-to-continuum ratio expected from ionized hydrogen at a temperature near 10,000 K. At 50 km/s resolution, the line is resolved with a FWHM of 200 km/s. Ten micron photometry clearly establishes a connection between G25.5+0.2 and the IRAS source 18344–0632. Most important, the infrared image reveals a point source in the center of the nebula that has properties of a blue luminous star that could excite an ionized ring nebula with the observed radio properties. The supernova hypothesis is ruled out and G25.5+0.2 is almost certainly a ring nebula around a mass losing luminous blue star ˜13 kpc distant and reddened by 20 magnitudes of visual extinction.

INTRODUCTION

Cowan et al. (1989) reported extensive observations of the galactic radio source G25.5+0.2. These included radio continuum images at four frequencies, 21 cm absorption measurements, and a search for radio recombination line emission. Based primarily on the absence of the H76α recombination line, Cowan et al. concluded that G25.5+0.2 is a very young galactic supernova remnant, perhaps only 25 years old. Based on 21 cm HI absorption lines, Cowan et al. give a minimum distance to G25.5+0.2 of 7.2 kpc. White and Becker (1990) and Green (1990) suggest that identification of G25.5+0.2 as a planetary nebula is more likely, based on the radio observations and IRAS fluxes.

INTRODUCTION

The nature of turbulent magnetic diffusion and the α-effect has been a puzzle for several decades. Until recently, virtually all the work in this subject has been based on analytical theory, but the advent of ready access to supercomputers now allows us to address the question of turbulent magnetic diffusion and the turbulent α-effect from the perspective of numerical experiments. In this paper, we shall describe numerical simulations of an idealized model of mean field dynamos.

In order to understand how fields are generated, the mean field theoretical approach is widely used (see Moffatt 1978). This two-scaled approach conveniently parametrizes the effects of small scale turbulence on large scale fields into two coefficients, α and β. The central problem of mean field electrodynamics is to calculate these transport coefficients from the statistical properties of the flow and the magnetic diffusivity, η. Explicit in these calculations is that the fluid flow is not affected by the presence of magnetic fields.

In typical magnetofluid circumstances, this is assumed to be the case, unless the magnetic energy of the large scale component is comparable to the energy in the flow. Recent two-dimensional simulations suggest that this is not the case and that turbulent diffusivity can be severely suppressed even when the mean field is less than the equipartition field value (see Cattaneo & Vainshtein 1991).

INTRODUCTION

An interesting asymptotic limit in the theory of dynamical systems enforces a highly-developed chaotic structure by the assumption of large-amplitude particle excursion in flows and maps. An example of such a method applied to diffusion of a scalar is given by Rechester & White (1980). This important idea has been developed by Soward (1992) in the context of fast dynamo theory and in particular for the case of pulsed helical waves. Our purpose in this note is to apply the large-amplitude method of Soward (1992), to the simpler SFS map (Bayly & Childress 1987, 1988). In the SFS (stretchfold- shear) map, a simple baker's map in the xy-plane is supplemented by a lateral shear in the z-direction. Numerical calculations indicate that, when the map operates in a perfectly conducting fluid on a magnetic field of the form (B(y)eikz, 0, 0), the average of the field over planes z=constant can be made to grow exponentially for sufficiently large shear. This property of ‘perfect’ fast dynamo action has never been proved in the SFS problem, however, despite the existence of an especially simple adjoint eigenvalue problem, where the growing eigenfunctions, if they exist, are known to be smooth (Bayly & Childress 1988). Moreover, numerical studies show clearly the existence of these eigenfunctions for the perfect fast dynamo problem.