  We consider how information on geostrophic flows in the planetary cores,
taken from 3D simulations in the sphere, can be used in 2D Parker's geodynamo
model with the simple forms of the $\alpha$-quenching. Using cluster computer
systems dependence of dynamo equations solution on the magnitudes of $\alpha$-
and $\omega$-effects is studied. We show that geostrophical flow can produce
the well-known Z-structure of the poloidal magnetic field without the feed-back
of the magnetic field onto the large-scale velocity field. The influence of
fluctuations of $\alpha$-effect on magnetic field generation, its spectral
properties, in respect to the geodynamo applications, is also discussed.
