摘要:

We deduce the dissipative Alfvén wave equation in a medium stratified in one direction, with a transverse magnetic field, in the presence of dissipation by fluid viscosity and electrical resistance; the dissipative Alfvén wave equation generalizes earlier results for homogeneous (Cowling, 1960) and inhomogeneous (Campos, 1983a) media, and corrects an error in the literature (Heyvaerts and Priest, 1983). The wave equation is solved exactly in two cases: a uniform magnetic field, and a magnetic field decreasing with height. In both cases the mean state is assumed to be isothermal, with a constant rate of ionization, so that the magnetic diffusivity is constant, but the dynamic viscosity increases with height. There are therefore two regions, a low- (high-) altitude region where electrical resistance dominates fluid viscosity (or vice versa), and an asymptotic regime relevant to the uppermost (lowermost) layers. The two regions are separated by a transition layer, across which the wave field is continuous and whose structure is expressible by hypergeometric functions, with different arguments in the low- and high-altitude regions, and over the whole altitude range. These exact solutions allow the amplitude and phase of the wave field to be plotted as a function of height for a variety of magnetoatmospheric mean states. They show that wave dissipation is more localized and intense when the magnetic field decreases with height than when it is uniform.

ISSN:0309-1929    

DOI:10.1080/03091928908218529

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

We introduce a general expansion approach to obtain a fully consistent closed set of magnetohydrodynamic equations in two independent variables, which is particularly useful to describe axially symmetric, time-dependent problems with weak variation of all quantities in the radial direction. This is done by considering the hierarchy of expanded magnetofluid equations in cylindrical coordinates and equating terms with equal powers in the radial coordinater. From geometrical considerations it is shown that the radial expansions of the pertaining physical quantities are either even series or odd series inr; this introduces a significant reduction in the number of variables and equations. The closure of the system is provided by appropriate boundary conditions. Among other possible applications, the method is relevant for the analysis of structure and dynamics of magnetic field concentrations in stellar atmospheres.

ISSN:0309-1929    

DOI:10.1080/03091928908218530

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Accretion disk material differs from normal stellar gas by the existence of the small-scale ‘‘α-turbulence'’ which enables the disk to form. This background turbulence transports both angular momentum in the radial direction and energy in the vertical direction, and at the same time produces heat by friction through its own eddy viscosity. The questions are whether in such a medium a convective instability with moderate scale-length would develop, and what form the instability (‘‘Schwarzschild'') criterion for such a convective motion would take. We find that the interaction of rotation and turbulence is an effective generator of (axisymmetric) instabilities even for the temperature gradients which normally, according to the traditional Schwarzschild criterion, guarantee stability. For different reasons, however, the new instabilities seem to be of minor relevance for modelling the thin accretion disks that in reality exist. Only in one case, in which the turbulent energy transport influences the fluctuations, does a convection develop for parameter values which are interesting in accretion disk theory.

ISSN:0309-1929    

DOI:10.1080/03091928908218531

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

We consider the topological relationship between magnetic field lines and magnetic flux surfaces. Magnetic helicity provides the most elementary description of the topology of magnetic field lines in terms of their linkage. In a simply-connected volume, a sufficient but not necessary condition for the total magnetic helicity to vanish is that there exist two independent families of globally-extendable flux surfaces (given by the level surfaces of Euler potentials). In contrast, the existence of two distinct global Euler potentials for multiply-connected volumes is insufficient to guarantee that the total magnetic helicity vanishes. These well-known results are discussed in the context of Frobenius’ theorem as applied to the differential equations describing magnetic lines of force; and the notion of Euler potentials is extended by introducing an analogy to the Hopf map between the three-sphere and the two-sphere.

ISSN:0309-1929    

DOI:10.1080/03091928908218532

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

In the last few years seismologists have proposed core-mantle topographies. At the same time much effort has been devoted by geomagneticians to calculate the fluid flow (and the related pressure field) at the top of the core, based on the observation of the secular variation of the geomagnetic field. A ‘‘topographic torque'', which results from the action of the pressure field at the core surface, has long been invoked to allow for exchanges of angular momentum between the core and the mantle. In this paper, we show that this torque can be computed if forces at the top of the core are in geostrophic balance. The deep nature of this topographic torque can be understood only if one goes beyond the case of a pseudo-static equilibrium and considers explicitly the acceleration term in the equation of motion. We show that the pressure field acts in such a way as to accelerate a zonal flow consisting of cylindrical annuli. These annuli rotate like rigid bodies, with an angular velocity which depends on the distance to the rotation axis. Furthermore, we show that a gravity torque may also act on these same cylinders.

ISSN:0309-1929    

DOI:10.1080/03091928908218533

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor