Discrete and Continuous Dynamical Systems (2010)

Misleading Results

The following publication by Oberlack & Rosteck (2010) is misleading:
New statistical symmetries of the multi-point equations and its importance for turbulent scaling laws
http://aimsciences.org/article/doi/10.3934/dcdss.2010.3.451

Details are given in https://arxiv.org/abs/1412.3061
and more comprehensively in https://zenodo.org/record/1101198#.WlNejmeUhaQ

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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 optimal systems of subalgebras for the equations of hydrodynamic stability analysis of smooth shear flows and their group-invariant solutions

Published in Journal of Mathematical Physics, 2017 by Hau, Oberlack & Chagelishvili. Apart from several technical mistakes and inconsistencies (please see Sec.4 in https://arxiv.org/abs/1712.03105 ), this study, initiated and supervised by M. Oberlack, is seriously misleading. Their claim that they have derived "a generalized approach" to stability analysis for unbounded shear flow that "unites both – the nonmodal (Kelvin mode) and the modal – approaches" for which "the class of solutions is much wider than the well-known Kelvin and modal solutions" is not correct and therefore misleading. First, their self-defined "modal approach" and "Kelvin mode approach" are complementary approaches, namely in being a pure temporal and a pure spatial approach respectively, which exclude each other and which therefore cannot be "united" into a single universal approach — this flaw is discussed in detail in Sec.4.2 in https://arxiv....
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