  In the study by Sadeghi & Oberlack [JFM 899, A10 (2020)] it is claimed that
new scaling laws are derived for the case of passive scalar dynamics under the
influence of a constant mean gradient in decaying homogeneous isotropic
turbulence. However, these scaling laws are not new and have already been
derived and discussed in Bahri (2016). No novel analytical achievements are
made by Sadeghi & Oberlack, as the title of their study misleadingly wants to
suggest. In fact, the already established self-similar scaling laws obtained by
Bahri through simple dimensional analysis are already more general in the
application than the ones obtained by Sadeghi & Oberlack through an overly
complicated and therefore unnecessarily performed Lie-group symmetry analysis.
The claim that it has the virtue of not being an ad-hoc method is not true.
Because, instead of using an a priori set of scales as the classical method,
the Lie-group method has to make use of an a priori set of symmetries, namely
to select the correct relevant symmetries from an infinite and thus unclosed
set. For example, a nonphysical scaling symmetry is selected which in the
course of the analysis has to be discarded since it is not compatible with the
data simulated. Hence, the Lie-group symmetry method in turbulence is just
another common trial-and-error method and not a first-principle method that can
bypass the closure problem.
