Symmetries and turbulence modeling

The study by Klingenberg, Oberlack & Pluemacher ["Symmetries and turbulence modeling", Phys. Fluids 32, 025108 (2020)] proposes a new strategy for modeling turbulence in general. A proof-of-concept is presented therein for the particular flow configuration of a spatially evolving turbulent planar jet flow, coming to the conclusion that their model can generate scaling laws which go beyond the classical ones. Our comment, however, shows that this is not the case. Hence, their argument of having established a new and more advanced turbulence model cannot be confirmed. The problem is already rooted in the modeling strategy itself, in that a nonphysical statistical scaling symmetry gets implemented. Breaking this symmetry will restore the internal consistency and will turn all self-similar solutions back to the classical ones. To note is that their model also includes a second nonphysical symmetry. One of the authors already acknowledged this fact in a former publication [Sadeghi, Oberlack & Gauding, "On new scaling laws in a temporally evolving turbulent plane jet using Lie symmetry analysis and direct numerical simulation -- Corrigendum", J. Fluid Mech. 885, E1 (2020)]. However, the Corrigendum is not cited and so the reader is not made aware that their method has fundamental problems that lead to inconsistencies and conflicting results. Instead, the very same nonphysical symmetry gets published again.