Parker's model in geodynamo

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.