  Direct numerical simulations of isotropically forced homogeneous stationary
turbulence with an imposed passive scalar concentration gradient are compared
with an analytical closure model which provides evolution equations for the
mean passive scalar flux and variance. Triple correlations of fluctuations
appearing in these equations are described in terms of relaxation terms
proportional to the quadratic correlations. Three methods are used to extract
the relaxation timescales tau_i from direct numerical simulations. Firstly, we
insert the closure ansatz into our equations, assume stationarity, and solve
for tau_i. Secondly, we use only the closure ansatz itself and obtain tau_i
from the ratio of quadratic and triple correlations. Thirdly we remove the
imposed passive scalar gradient and fit an exponential decay law to the
solution.
  We vary the Reynolds (Re) and P\'eclet (Pe) numbers while keeping their ratio
at unity and the degree of scale separation and find for large Re fair
correspondence between the different methods. The ratio of the turbulent
relaxation time of passive scalar flux to the turnover time of turbulent eddies
is of the order of three, which is in remarkable agreement with earlier work.
Finally we make an effort to extract the relaxation timescales relevant for the
viscous and diffusive effects. We find two regimes which are valid for small
and large Re, respectively, but the dependence of the parameters on scale
separation suggests that they are not universal.
