We present simulations of the 3D nonlinear induction equation in order
to investigate the temporal evolution of large-scale magnetic fields
in spiral galaxies. Our model includes differential rotation, ambipola
r diffusion and, based on small-scale turbulence, eddy diffusivity and
the tensorial alpha-effect with magnetic feedback. The nonaxisymmetri
c spiral pattern and - if considered - the vertical stratification of
the galaxy are represented in its density and turbulence profile. Negl
ecting vertical stratification the lifetime and geometry of an initial
magnetic field depend on the correlation time of interstellar turbule
nce T-corr. Short correlation times increase the lifetime of the initi
al magnetic field, but the field is rapidly wound pip. Its pitch-angle
s develop to zero. The magnetic field has disappeared after at most 1
to 1.5 Gyr. A resonance like phenomenon is found by tuning the pattern
velocity of the galactic spiral. The simulations then show an excepti
onal amplification of the magnetic field in the case that the pattern
speed and a magnetic drift velocity have similar values. Considering a
vertical stratification we achieve sufficiently long living grand-des
igned magnetic fields excited by dynamo action. The behaviour and geom
etry of the resulting field is again significantly influenced by the c
orrelation time T-corr. Small values of T-corr lead to axisymmetric fi
elds with small pitch-angles and field-concentration between the spira
l arms. Increasing the correlation time the solutions show larger pitc
h-angles; and depending on very large correlation times the galactic d
ynamo rather generates fields clearly within the spiral arms and havin
g a bisymmetric structure.