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The self-similarity of a passive scalar in homogeneous isotropic decayingturbulence 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 highlyresolved direct numerical simulation of decaying turbulence. The method of linesegments is used to perform a decomposition of the scalar field into smallersub-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 endingpoints. Line segments can be understood as thin local convective-diffusivestructures in which diffusive processes are enhanced by compressive strain.From DNS, it is shown that the marginal distribution function of thelength~$\ell$ assumes complete self-similarity when re-scaled by the meanlength $\ell_m$. The joint statistics of $\Delta\phi$ and $\ell$, from whichthe local gradient $g=\Delta\phi/\ell$ can be defined, play an important rolein understanding the turbulence mixing and flow structure. Large values of $g$occur at a small but finite length scale. Statistics of $g$ are characterizedby rare but strong deviations that exceed the standard deviation by more thanone order of magnitude. It is shown that these events break completeself-similarity of line segments, which confirms the standard paradigm ofturbulence that intense events (which are known as internal intermittency) arenot self-similar.

On the self-similarity of line segments in decaying homogeneous isotropic turbulence