A closer look at predicting turbulence statistics of arbitrary moments when based on a non-modelled symmetry approach

TL;DR

This paper critically examines a recent claim that symmetry-based solutions of turbulence equations can predict turbulence statistics accurately, arguing that the method is flawed and does not provide a first-principles solution.

Contribution

The paper refutes previous claims of symmetry-based turbulence solutions, clarifying that the approach cannot bypass turbulence closure problems and is not a first-principles method.

Findings

Symmetry-induced scaling laws cannot fit Reynolds-stress data.

The method does not solve the turbulence closure problem.

Previous claims of breakthroughs are misleading.

Abstract

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.