  We study the spatio-temporal two-point correlation function of passively
advected scalar fields in the inertial-convective range in three dimensions by
means of numerical simulations. We show that at small time delays $t$ the
correlations decay as a Gaussian in the variable $tp$ where $p$ is the
wavenumber. At large time delays, a crossover to an exponential decay in $tp^2$
is expected from a recent functional renormalization group (FRG) analysis. We
study this regime for a scalar field advected by a Kraichnan's ``synthetic''
velocity field, and accurately confirm the FRG result, including the form of
the prefactor in the exponential. By introducing finite time correlations in
the synthetic velocity field, we uncover the crossover between the two regimes.
