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 α 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 α-effect
is essentially magnified in the spiral arms and diminished in the interarm
regions, what confirms our previous results obtained in the linear
approximation.Comment: LaTeX, 13 pages, 15 ps figures, uses l-aa.sty and epsf.sty. Published
in Astronomy & Astrophysics, 327, 81