We use the Lie symmetry theory to derive new scaling laws for passive scalar dynamics
under the influence of a constant mean gradient of the scalar in decaying homogeneous
isotropic turbulence. For this purpose, we apply symmetry analysis to the equations for two-
point correlation of the scalar and velocity fluctuations. It is shown that, in contrast to the
classical self-similarity approach, the general invariant solutions, respectively scaling laws,
of the two-point functions are constructed using the symmetry approach, without requiring an …

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 …