  Using N-body simulations of the Galactic disks, we qualitatively study how
the metallicity distributions of the thick and thin disk stars are modified by
radial mixing induced by the bar and spiral arms. We show that radial mixing
drives a positive vertical metallicity gradient in the mono-age disk population
whose initial scale-height is constant and initial radial metallicity gradient
is tight and negative. On the other hand, if the initial disk is flaring, with
scale-height increasing with galactocentric radius, radial mixing leads to a
negative vertical metallicity gradient, which is consistent with the current
observed trend. We also discuss impacts of radial mixing on the metallicity
distribution of the thick disk stars. By matching the metallicity distribution
of N-body models to the SDSS/APOGEE data, we argue that the progenitor of the
Milky Way's thick disk should not have a steep negative metallicity gradient.
