The galactic dynamo effect due to Parker-shearing instability of magnetic flux tubes II. Numerical simulations and the nonlinear evolution

In this paper we continue investigations of the Parker-shearinginstabilityperformingnumericalsimulationsof the magnetic flux tube dynamics in the thin flux-tube approx- imation. 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 sin- gularity 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 wave- length 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 efcient than that related to the linearly most un- stable 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 mag- nied in the spiral arms and diminished in the interarm regions, what conrms our previous results obtained in the linear ap- proximation.