2 research outputs found
Mean--field electrodynamics: Critical analysis of various analytical approaches to the mean electromotive force
There are various analytical approaches to the mean electromotive force crucial in mean--field electrodynamics, with
and
being velocity and magnetic field fluctuations. In most cases the
traditional approach, restricted to the second--order correlation
approximation, has been used. Its validity is only guaranteed for a range of
conditions, which is narrow in view of many applications, e.g., in
astrophysics. With the intention to have a wider range of applicability other
approaches have been proposed which make use of the so--called
--approximation, reducing correlations of third order in and
to such of second order. After explaining some basic features of the
traditional approach a critical analysis of the approaches of that kind is
given. It is shown that they lead in some cases to results which are in clear
conflict with those of the traditional approach. It is argued that this
indicates shortcomings of the --approaches and poses serious restrictions
to their applicability. These shortcomings do not result from the basic
assumption of the --approximation. Instead, they seem to originate in
some simplifications made in order to derive without really solving
the equations governing and . A starting point for a new
approach is described which avoids the conflict.Comment: 32 pages, no figures; accepted by Geophys. Astrophys. Fluid Dynam. A
quenching formula for \alpha and a section on comparisons with numerical
simulations added; references amended; changes in presentation and languag
Contributions to the theory of a two-scale homogeneous dynamo experiment
The principle of the Karlsruhe dynamo experiment is closely related to that
of the Roberts dynamo working with a simple fluid flow which is, with respect
to proper Cartesian co-ordinates x, y and z, periodic in x and y and
independent of z. A modified Roberts dynamo problem is considered with a flow
more similar to that in the experimental device. Solutions are calculated
numerically, and on this basis an estimate of the excitation condition of the
experimental dynamo is given. The modified Roberts dynamo problem is also
considered in the framework of the mean-field dynamo theory, in which the
crucial induction effect of the fluid motion is an anisotropic alpha-effect.
Numerical results are given for the dependence of the mean-field coefficients
on the fluid flow rates. The excitation condition of the dynamo is also
discussed within this framework. The behavior of the dynamo in the nonlinear
regime, i.e. with backreaction of the magnetic field on the fluid flow, depends
on the effect of the Lorentz force on the flow rates. The quantities
determining this effect are calculated numerically. The results for the
mean-field coefficients and the quantities describing the backreaction provide
corrections to earlier results, which were obtained under simplifying
assumptions.Comment: 12 pages, 9 figures, accepted for publication in Phys. Rev.