A number of different simulations have now established the possibility
to generating strong large scale magnetic fields from turbulent motions
(Glatzmaier & Roberts 1995; Brandenburg et al. 1995; Ziegler & Rüdiger 2000;
Brandenburg 2001, hereafter referred to as B2001).
Although most of these simulations were devised to
explain magnetism in real astrophysical bodies, it remains debatable
whether or not the mechanisms that are at work in those simulations are
also those that are responsible for the generation of large scale fields
in astrophysical bodies. Up to modestly high
magnetic Reynolds numbers, currently accessible to simulations, the by far strongest
large scale dynamo effect is based on kinetic helicity of the flow.
This effect is described in standard text books (e.g. Moffatt 1978;
Krause & Rädler 1980), and is closely related to the inverse cascade
of magnetic helicity (Frisch et al. 1975; Pouquet et al. 1976). The
reason why one may suspect problems with such mechanisms in astrophysical
settings is that they tend to produce large scale magnetic fields that
are helical and that, owing to magnetic helicity conservation, such
helical fields can only be built up slowly on a resistive time scale
(B2001). Of course,
shear (or differential rotation) contributes strongly to the dynamo
and enhances the growth rate and final field strength, but this reduces the
resistively limited saturation
time of the dynamo only by a factor of 10-100 for the Sun
(Brandenburg et al. 2001, hereafter referred to as BBS2001),
or perhaps somewhat more for accretion discs. Typical growth times
will still be of the order of
.
Open boundaries
also tend to reduce the time scale, but this is typically at the expense of lowering the
final field strength (Brandenburg & Dobler 2001, hereafter referred
to as BD2001).
The "helicity problem'' was originally identified in attempts to
understand the "catastrophic'' magnetic feedback on turbulent transport
coefficients such as turbulent diffusivity (Cattaneo & Vainshtein 1991)
and the alpha-effect (Vainshtein & Cattaneo 1992;
Cattaneo & Hughes 1996). Although the original
arguments did not invoke magnetic helicity, subsequent work by
Bhattacharjee & Yuan (1995) and Gruzinov & Diamond (1995) related
the quenching to helicity conservation. Furthermore,
models using the proposed
quenching formulae reproduce the field evolution in the simulations
and those predicted by magnetic helicity conservation extremely well
(B2001, Fig. 21). Blackman & Field (2000) pointed out that
catastrophic quenching of the 
-effect is peculiar to
flows in periodic domains where there is no loss of magnetic helicity.
It is important to emphasise that the helicity problem applies to the
non-kinematic stage of dynamo activity, without explicitly
invoking the concept of -effect dynamos.
A possible way out of the helicity problem is to produce large scale fields
without invoking kinetic helicity of the flow. That helicity is not
crucial for large scale dynamo action was already known since the
work of Gilbert et al. (1988), who found that flows that only lack parity invariance are
already capable of producing large scale dynamo action via an -effect.
The problem has
been investigated further in a recent paper by Zheligovsky et al. (2001),
who found that even parity invariant flows are capable of large-scale
dynamo action. In that case the dynamo works not via an -effect,
but through a negative turbulent magnetic diffusivity effect.
A related issue was brought up by Vishniac & Cho (2001,
hereafter referred to as VC2001)
in an attempt to produce large scale non-helical dynamo action
that would survive in the large magnetic Reynolds number limit.
Their mechanism requires the presence of a certain correlation between
the azimuthal component of the vorticity and the azimuthal gradient of
the vertical velocity. If that is the case they predict the presence of
a strong vertical magnetic helicity current upwards. This could then drive a
field-aligned electromotive force that is proportional to the divergence
of this magnetic helicity current. This form of the electromotive force
would conserve magnetic helicity and was first proposed by Bhattacharjee
& Hameiri (1986).
The purpose of the present paper is to assess the viability and properties of the mechanism proposed by VC2001 using numerical simulations. The required correlation between the azimuthal derivative of the vertical velocity and the azimuthal component of the vorticity is expected to occur in the presence of shear. It should thus be especially important in accretion discs. We therefore begin by determining the presence of such a correlation using global simulations of accretion discs (Sect. 2).
However, in order to isolate the proposed effect from the ordinary helicity effect, which is always present because of rotation, we have also carried out some idealized simulations of forced turbulence with shear, but no rotation. The latter is expected to promote the correlation anticipated by VC2001, but would not lead to kinetic helicity in the flow. Of course, real systems do rotate and have therefore also kinetic helicity. However, at small and modestly large magnetic Reynolds numbers the dynamo effect based on kinetic helicity is so much more powerful than other mechanisms that it is necessary to suppress it artificially if one wants to study it in isolation. This will be done in Sect. 3.
For both the global disc simulations as well as the idealized model we also determine the resulting helicity fluxes, which turn out to be small and fluctuating about zero, however. We conclude in Sect. 4 with summarizing remarks and speculations concerning the viability of conventional helicity-driven dynamos.
Copyright ESO 2001