Symmetries and the closure problem of turbulence

https://doi.org/10.5281/zenodo.1116165

The above link is a collection of examinations showing that the closure problem of turbulence cannot be "somewhat bypassed" by formally considering the infinite set of correlation equations and its admitted set of symmetries, as misleadingly claimed by the group of Oberlack et al. ➽

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Symmetries and turbulence modeling

Published in  Physics of Fluids, 2020  by Klingenberg, Oberlack & Pluemacher. This publication is seriously misleading and flawed. All details and corrections are given in  https://arxiv.org/abs/2008.08580 , and more comprehensively in  https://doi.org/10.5281/zenodo.4275736 .
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On the Lie symmetries of characteristic function hierarchy in compressible turbulence

Published in European Journal of Applied Mathematics, 2022  by Praturi, Plümacher & Oberlack. All problems that one encounters in the incompressible case translate here one-to-one to the compressible case: A symmetry analysis of an unclosed system with an infinite hierarchy is performed again, leading to two nonphysical "symmetries" (4.17) and (4.18), where the latter one is incorrectly elevated again to a symmetry that should reflect external intermittency in turbulent flows. But, exactly as in the incompressible case, these two "symmetries" are just mathematical artefacts of the unclosed equations and not reflected by experiment or numerical simulation. They both fail to model turbulence or to derive turbulent scaling laws that can be matched to relevant data. The scaling failure in the incompressible case is explicitly shown in https://doi.org/10.1017/jfm.2019.985 ,  https://arxiv.org/abs/1412.3061 ,  https://arxiv.org/abs/1606.08396 ,  https://doi....
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Group analysis, direct numerical simulation and modelling of a turbulent channel flow with streamwise rotation

Published in JFM, 2006 by Oberlack, Cabot, Pettersson-Reif & Weller. This publication is misleading and flawed. Apart from various mathematical errors, this study is altogether inconsistent in its Lie-group symmetry part. In addition it also contains several non-reproducible conclusions. All details and corrections to this flawed study are given in https://arxiv.org/abs/1609.08155 .
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