摘要:

This volume contains the Proceedings of the US-Russian conference on Magneto-hydrodynamic Stability and Dynamos held at the Mathematics Department of the University of Chicago from 21st May to 26th May 1992. Originally the conference was planned to be held in Moscow in August 1991. Because of political developments at that time in Russia, the location of the conference was changed to Chicago. We would like to thank Professor V.I. Keilis-Borok, Director of M.I.T.P.A.N. in MOSCOW, for his full support during the initial planning stage for the conference.

ISSN:0309-1929    

DOI:10.1080/03091929308203616

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The dynamo problem is considered for mappings with pulsed diffusion in the fast dynamo limit of vanishing magnetic diffusion. It is shown how the determinant of a dynamo operator may be expanded in terms of sums over the periodic orbits of the mapping. In mappings for which all the orbits are hyperbolic the limit of weak diffusion may be taken formally, yielding a prescription for calculating the fast dynamo growth rate from information about the periodic orbits. A mathematical justification for taking the limit of weak diffusion has not been obtained. Nevertheless it is verified that the prescription for calculating fast dynamo growth rates from periodic orbit sums gives correct growth rates for a number of models, including stretch-fold-shear and cat maps with shear.

ISSN:0309-1929    

DOI:10.1080/03091929308203617

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The large time asymptotics of a magnetic field in a turbulent δ-correlated (in time) flow of an ideal incompressible fluid are studied. It is shown that the magnetic field exhibits the dynamo effect (exponential stretching) unless the Lagrangian flow generated by the velocity field is (almost surely) distance preserving; and it is intermittent unless the Lagrangian flow associated to the turbulent component of the velocity is (almost surely) distance preserving.

ISSN:0309-1929    

DOI:10.1080/03091929308203618

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The equation (δt+u·∇)C=R(x,t)C+ k∇2C, is a scalar analogue of the magnetic induction equation. If the velocity fieldu(x,t) and the ‘stretching’ functionR(x,t) are explicitly given, then we have the analogue of the dynamo problem. The scalar problem displays many of the same features as the vector kinematic dynamo problem. The fastest growing modes have growth rates that approach a finite limit asK→0 while the eigenfunctions develop more and more complex structure at smaller and smaller length scales. Some insight is provided by an analysis which finds a lower bound on the growth rate that is asymptotically independent of the diffusivity.

ISSN:0309-1929    

DOI:10.1080/03091929308203619

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

This paper considers the fast dynamo problem for chaotic flows which are close to integrable. The basic example is a time-dependent cat's eye flow whosex − y(horizontal) components are generated by the streamfunction

ISSN:0309-1929    

DOI:10.1080/03091929308203620

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

We present a simple combinatorial theorem in the theory of weighted, framed links which is, broadly speaking, consistent with J. B. Taylor's theory of magnetic relaxation (Taylor, 1986). In this theory magnetic helicity plays a preferred role, decaying on the diffusive timescale whereas other topological invariants and the magnetic energy are presumed to decay much more quickly. Upper limits can be placed on the helicity dissipated during a fixed time interval in an isolated magnetised plasma (Berger, 1984). These upper limits vary as η½ (η = resistivity) and hence vanish in the limit η→0. On the other hand, finite energy dissipation may well be possible in that limit; processes which liberate energy on dynamic rather than resistive timescales are known as rapid (or fast) reconnection (Forbes and Priest, 1987). Solar flares, for example, would be difficult to explain without invoking rapid reconnection.

ISSN:0309-1929    

DOI:10.1080/03091929308203621

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

A sufficient condition for instability of the Euler equations [see (1.5)] is used to demonstrate the instability of certain ABC flows. In the parameter rangeA= 1,B2+C2> 1, instability follows from the presence of hyperbolic stagnation points. In the parameter rangeA= 1,B=C= «ϵ1, instability follows from the existence of hyperbolic closed trajectories and the associated exponential stretching of the fluid particles. This result is proved analytically in Section 2 and illustrated numerically via Poincaré sections in Section 3.

ISSN:0309-1929    

DOI:10.1080/03091929308203622

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

Two dimensional ideal incompressible MHD turbulence is studied in a Lagrangian framework in which the non-local pressure forces are approximated to be locally isotropic. Within this model current sheet formation at null points and along field lines is observed. In the case of field lines, this behavior is found to be robust under addition of random pressure fluctuations from isotropy. The value of a quantity called the fluid balance of strain is found to be important in predicting where and when current sheet formation occurs.

ISSN:0309-1929    

DOI:10.1080/03091929308203623

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

We study the spectrum of the operator describing the growth of magnetic fields in an infinitely conducting, incompressible fluid. We show that, in many circumstances, it consists of an annulus and also give characterization of this spectrum by the Lyapunov exponents of periodic orbits of the Lagrangian flow. We also consider the effect on the spectrum of considering only spaces of vector fields with zero divergence—a physically reasonable restriction for magnetic fields—and find that, for many systems, even if the outer edges of the spectrum are not changed, there appear non-trivial components of residual spectrum.

ISSN:0309-1929    

DOI:10.1080/03091929308203624

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

We solve the fast dynamo problem for any smooth map on the two-torus. In particular, we prove that the fast dynamo exponent is equal to the asymptotic Lefschetz number. We also find the form of the leading eigenfunction. The eigenfunction for positive diffusivity is a smoothened version of a diffusionless eigen-function.

ISSN:0309-1929    

DOI:10.1080/03091929308203625

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor