  The mean electromotive force and alpha effect are computed for a forced
turbulent flow using a simple nonlinear dynamical model. The results are used
to check the applicability of two basic analytic ansatze of mean-field
magnetohydrodynamics - the second order correlation approximation (SOCA) and
the tau approximation. In the numerical simulations the effective Reynolds
number Re is 2-20, while the magnetic Prandtl number varies from 0.1 to
$10^{7}$. We present evidence that the $\tau$ approximation may be appropriate
in dynamical regimes where there is a small-scale dynamo. Catastrophic
quenching of the $\alpha$ effect is found for high $P_{m}$. Our results
indicate that for high $P_{m}$ SOCA gives a very large value of the $\alpha$
coefficient compared with the ``exact'' solution. The discrepancy depends on
the properties of the random force that drives the flow, with a larger
difference occuring for $\delta$-correlated force compared with that for a
steady random force.
