  Transport equations for even-order structure functions are written for a
passive scalar mixing fed by a mean scalar gradient, with a Schmidt number
$\mathit{Sc}=1$. Direct numerical simulations (DNS), in a range of Reynolds
numbers $R_\lambda \in [88,529]$ are used to assess the validity of these
equations, for the particular cases of second-and fourth-order moments. The
involved terms pertain to molecular diffusion, transport, production, and
dissipative-fluxes. The latter term, present at all scales, is equal to: i) the
mean scalar variance dissipation rate, $\langle \chi \rangle$, for the
second-order moments transport equation; ii) non-linear correlations between
$\chi$ and second-order moments of the scalar increment, for the fourth-order
moments transport equation. The equations are further analyzed to show that the
similarity scales (i.e., variables which allow for perfect collapse of the
normalised terms in the equations) are, for second-order moments, fully
consistent with Kolmogorov-Obukhov-Corrsin (KOC) theory. However, for
higher-order moments, adequate similarity scales are built from $\langle \chi^n
\rangle$. The similarity is tenable for the dissipative range, and the
beginning of the scaling range.
