  A recent Letter by Oberlack et al. [Phys. Rev. Lett. 128, 024502 (2022)]
claims to have derived new symmetry-induced solutions of the non-modelled
statistical Navier-Stokes equations of turbulent channel flow. A high accuracy
match to DNS data for all streamwise moments up to order 6 is presented, both
in the region of the channel-center and in the inertial sublayer close to the
wall. Here we will show that the findings and conclusions in that study are
highly misleading, as they give the impression that a significant breakthrough
in turbulence research has been achieved. But, unfortunately, this is not the
case. Besides trivial and misleading aspects, we will demonstrate that even
basic turbulence-relevant correlations as the Reynolds-stress cannot be fitted
to data using the proposed symmetry-induced scaling laws. The Lie-group
symmetry method as used by Oberlack et al. cannot bypass the closure problem of
turbulence. It is just another assumption-based method that requires modelling
and is not, as claimed, a first-principle method that leads directly to
solutions. Next to PRL, two more papers by Oberlack et al. are called out for
correction or a retraction.
