*Astron. Astrophys. 327, 813-824*
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## The galactic dynamo effect due to Parker-shearing
instability of magnetic flux tubes
### II. Numerical simulations and the nonlinear evolution
**M. Hanasz**
Centre for Astronomy, Nicolaus Copernicus University,
PL-87148 Piwnice/Torun, Poland (e-mail: mhanasz@astri.uni.torun.pl)
*Received 26 November 1996 / Accepted 27 May 1997*
**Abstract**
In this paper we continue investigations of the Parker-shearing instability
performing numerical simulations of the magnetic flux tube dynamics in the thin
flux-tube approximation. We show that evolution of flux tubes resulting
from numerical simulations is very similar to that of linear solutions if the
vertical displacements are smaller than the vertical scale height *H* of the
galactic disc. If the vertical displacements are comparable to *H*, the
vertical growth of perturbations is faster in the nonlinear range than in the
linear one and we observe a rapid inflation of the flux tube at its top,
which leads to a singularity in numerical simulations, if only the cosmic rays
are taken into account. Then we perform simulations for the case of nonuniform
external medium, which show that the dominating wavelength of the Parker
instability is the same as the wavelength of modulations of external medium.
As a consequence of this fact, in the case of dominating cosmic ray pressure,
the dynamo effect related to these short wavelength modulations is
much more efficient than that related to the linearly most unstable long
wavelengths modes of the Parker instability. Under the influence of
differential forces resulting from differential rotation and the density waves,
the -effect is essentially magnified in the spiral arms and
diminished in the interarm regions, what confirms our previous
results obtained in the linear approximation.
**Key words: **instabilities - MHD - galaxies: magnetic fields
- ISM: kinematics and dynamics
*Send offprint requests to:* M. Hanasz
© European Southern Observatory (ESO) 1997
Online publication: October 14, 1997
Last change: April 6, 1998
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