  A mean-field theory of the electrodynamics of a turbulent fluid is formulated
under the assumption that the molecular electric conductivity is correlated
with the turbulent velocity fluctuation in the (radial) direction,
$\mathbf{g}$. It is shown that for such homogeneous fluids a strong
turbulence-induced field advection anti-parallel to $\mathbf{g}$ arises almost
independently of rotation. For rotating fluids, an extra $\alpha$ effect
appears with the known symmetries and with the expected maximum at the poles.
Fast rotation, however, with Coriolis number exceeding unity suppresses this
term. Numerical simulations of forced turbulence using the NIRVANA code
demonstrate that the radial advection velocity, $\gamma$, always dominates the
$\alpha$ term. We show finally with simplified models that $\alpha^2$ dynamos
are strongly influenced by the radial pumping: for $\gamma<\alpha$ the
solutions become oscillatory, while for $\gamma>\alpha$ they become highly
exotic if they exist at all. In conclusion, dynamo models for slow and fast
solid-body rotation on the basis of finite conductivity-velocity correlations
are unlikely to work, at least for $\alpha^2\Omega$ dynamos without strong
shear.
