  The self-similarity of a passive scalar in homogeneous isotropic decaying
turbulence is investigated by the method of line segments (M. Gauding et al.,
Physics of Fluids 27.9 (2015): 095102). The analysis is based on a highly
resolved direct numerical simulation of decaying turbulence. The method of line
segments is used to perform a decomposition of the scalar field into smaller
sub-units based on the extremal points of the scalar along a straight line.
These sub-units (the so-called line segments) are parameterized by their length
$\ell$ and the difference $\Delta\phi$ of the scalar field between the ending
points. Line segments can be understood as thin local convective-diffusive
structures in which diffusive processes are enhanced by compressive strain.
From DNS, it is shown that the marginal distribution function of the
length~$\ell$ assumes complete self-similarity when re-scaled by the mean
length $\ell_m$. The joint statistics of $\Delta\phi$ and $\ell$, from which
the local gradient $g=\Delta\phi/\ell$ can be defined, play an important role
in understanding the turbulence mixing and flow structure. Large values of $g$
occur at a small but finite length scale. Statistics of $g$ are characterized
by rare but strong deviations that exceed the standard deviation by more than
one order of magnitude. It is shown that these events break complete
self-similarity of line segments, which confirms the standard paradigm of
turbulence that intense events (which are known as internal intermittency) are
not self-similar.
