The self-similarity of a passive scalar in homogeneous isotropic decaying tumultuousturbulence is investigated by the method of line segments. The analysis is based on a highly resolved direct numerical simulation of decaying turbulence.
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
and the difference 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~ assumes complete self-similarity when re-scaled by the mean
length . The joint statistics of and , from which
the local gradient can be defined, play an important role
in understanding the turbulence mixing and flow structure. Large values of
occur at a small but finite length scale. Statistics of 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