  Parker instability leads to the formation of tangential discontinuities in a
magnetic field and subsequent magnetic reconnection due to a numerical and/or
an explicit resistivity. In this paper we investigate the role of the uniform,
localized and numerical resistivity on the diffusion of magnetic field lines
during the growth phase of Parker instability modes. We propose a new method to
quantify the diffusion of magnetic field lines which is attributed to the
presence of resistivity in ideal and non-ideal MHD codes. The method relies (1)
on integration of magnetic lines in between periodic boundaries, (2) on
measurements of the dispersion of magnetic field lines with the left and the
right periodic boundaries and (3) on a statistical analysis of shifts of a
large set of magnetic lines. The proposed method makes it possible to detect
topological evolution of magnetic field. We perform a series of resistive MHD
simulations of the Parker instability in uniformly rotating galactic disks. We
follow the topological evolution of the magnetic field evolving due to the
Parker instability and relate it to the ratio of total to uniform magnetic
field in galactic disks. We find that after the onset of the Parker
instability, the magnetic field becomes first tangled and later on it evolves
toward a uniform state due to the presence of resistivity. A similar effect of
a varying contribution of a turbulent magnetic field is observed in arms and
inter-arm regions of galaxies.
