Turbulence & Symmetries

Published in Journal of Physics, 2011 by Oberlack & Rosteck. This study is misleading. It develops and derives misleading results. Details are given in  https://arxiv.org/abs/1412.3061 , and more comprehensively in  https://doi.org/10.5281/zenodo.1101197 .

Published in Springer Proceedings in Physics, 2019 by Klingenberg, Oberlack & Pluemacher. Anyone with experience in turbulence modelling immediately recognizes that this newly proposed turbulence model (Eqs.6-8,10) is a mathematical artefact without physical value. In a nutshell, here's the construction strategy of their newly proposed modelling principle: From the unclosed set of statistical equations, two arbitrary symmetries (Eqs.4-5) out of an infinite pool of possible symmetries are taken in order to modify existing turbulence models such that they now comply with these two particularly chosen symmetries. To achieve this, new mathematical field variables are introduced: The new velocity field $\boldsymbol{\frak{U}}$ and the new pressure field $\frak{P}$. Hence, when also including any underlying DNS data to these newly created statistical models, we basically are dealing here with three different velocity fields (and three different pressure fields accordingly):...

Published in JFM, 2018 by Sadeghi, Oberlack & Gauding. This study is flawed in facing the following severe problems: (1) The interpretations and conclusions in this study are not justified by the results given. Particularly, Fig.7 cannot be reproduced from the given DNS data shown in Fig.4(a-c) as claimed. The analytic asymptotic behaviours of the underlying equations (4.10-12) do not match the corresponding numerical asymptotic behaviours as shown in Fig.7: Firstly, when proposing the scaling (4.10-12), a collapse of the profiles for large $\tilde{x}_2$ cannot be confirmed and, secondly, in this regime the profiles also do not tend to zero as incorrectly shown in Fig.7. That the profiles for the invariantized diagonal Reynolds stresses do not collapse and do not tend to zero in the asymptotic regime when scaled as (4.10-12) can be easily seen by considering e.g. the case $\tilde{R}\vphantom{R}^0_{22}$ (4.11) — the reasoning for the other two cases (4.10) and (4.12...

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....

Published in Journal of Physics A, 2017 by Grebenev, Waclawczyk & Oberlack. This publication is seriously misleading and flawed. The conformal invariance for the Lundgren-Monin-Novikov vorticity equations cannot be confirmed. All details and corrections are given in https://arxiv.org/abs/1802.02490 , and more comprehensively in  https://doi.org/10.5281/zenodo.6228153 .

Published in Journal of Physics A, 2017 by Waclawczyk, Grebenev & Oberlack. This study faces three shortcomings: (1) Their analysis misses a very central aspect of the LMN equations which thus, opposite to their claim, makes their Lie-group symmetry results incomplete. (2) The statements on the constraints regarding the infinite-dimensional symmetry groups are misleading. (3) The particular scaling symmetry originating solely from the linearity of the LMN hierarchy is nonphysical in that it violates the classical principle of cause and effect. This fact was proven analytically in a rigorous manner in 2014: https://doi.org/10.1103/PhysRevE.92.067001 , https://arxiv.org/abs/1412.6949 , https://arxiv.org/abs/1412.3061 , https://arxiv.org/abs/1602.08039 . Details on (1): The LMN equations are always accompanied by at least five physical constraints in order to guarantee their solutions to be physical. These are the four well-known and so-called non-negativity, nor...

Published in JFM, 2017 by Dierkes & Oberlack. This investigation by Dierkes & Oberlack makes a few false and misleading statements which are worth to be pointed out. (1) Misleading is the following statement: "For three-dimensional time-dependent fluid flows, CLs [conservation laws] were studied in very much detail in Cheviakov & Oberlack (2014). Therein, they considered higher-order CL multipliers and obtained an infinite family of vorticity CLs" (p.345). What is misleading here is that it is not said that all these new CLs obtained in this way are ultimately all trivial in having no physical significance. The reason is that this infinite set of new conservation laws obtained by Cheviakov & Oberlack (2014) involve arbitrary functions of all independent variables (careful: not dependent, but independent ones), making them thus physically trivial. This was clearly shown by Rosenhaus & Shankar (Second Noether theorem for quasi-Noether systems, J...

Published in Journal of Physics, 2016 by Waclawczyk & Oberlack. This publication is seriously flawed, both methodologically as well as technically. For all details, please see https://www.researchgate.net/publication/311285232 . Nevertheless, it is worth to briefly list and summarize the most important errors of this publication in the order as they appear in the text: 1.  The two "new" additional symmetries (5) and (6) not only violate the separation constraint of the LMN equations, but also the causality principle of classical mechanics. For more details on this particular issue, please see https://doi.org/10.1103/PhysRevE.92.067001 and https://arxiv.org/abs/1602.08039 . 2. The mentioned modification on p.3 "due to the presence of boundaries" breaks the symmetry (6) not only for the unbounded, but also of the bounded LMN equations for channel flow. The proof to this statement can be found in https://arxiv.org/abs/1412.6949 and https://www.researchgat...

Published in Symmetry, 2016 by Waclawczyk, Janocha & Oberlack. This publication is seriously flawed. Apart from numerous mathematical errors, this study also contains several inconsistent conclusions. All details and corrections are given in https://www.researchgate.net/publication/301553065 .

Published in Journal of Mathematical Physics, 2016 by Waclawczyk & Oberlack. This publication is misleading and flawed. Apart from a major mathematical error, this study also contains several inconsistent conclusions. All details and corrections are given in https://www.researchgate.net/publication/299368809 .

Published in Physical Review E, 2015 by Waclawczyk & Oberlack. This publication is misleading and flawed. Apart from various mathematical errors, this study also contains several inconsistent conclusions. Details and corrections are given in https://www.researchgate.net/publication/287996194 , https://arxiv.org/abs/1602.08039 and https://arxiv.org/abs/1412.6949 .

Published in Symmetry, 2015 by Janocha, Waclawczyk & Oberlack. This publication is seriously flawed. Apart from numerous mathematical errors, this study is entirely inconsistent. Details and corrections are given in http://dx.doi.org/10.3390/sym8040023   and more comprehensively in  https://doi.org/10.5281/zenodo.1101170 .

Published in Mechanical Engineering Reviews, 2015 by Oberlack, Waclawczyk, Rosteck & Avsarkisov The reader is confronted here with a collection of articles showing the results obtained in the group of M. Oberlack during the years 2010-2015. In the last three years, however, several (peer-reviewed) Comments and Notes have been published that do not confirm these results: https://zenodo.org/communities/turbsym . Eventually all central results and conclusions by Oberlack et al. are based on the global methodological error that new statistical symmetries are produced that are not compatible to the deterministic description of Navier-Stokes turbulence. One of the latest investigations https://arxiv.org/abs/1606.08396 clearly reveals this fact again. Therein (viz. Section 5.2), particularly their results obtained in Sec.6.2 (pp.53-63) for a turbulent channel flow with constant wall-transpiration were revisited. As proven and demonstrated in detail, these results cannot be...

Published in Physical Review E, 2014 by Waclawczyk, Staffolani, Oberlack, Rosteck, Wilczek & Friedrich. This study is seriously misleading and flawed. Details and corrections are given in https://doi.org/10.1103/PhysRevE.92.067001   and more comprehensively in  https://doi.org/10.5281/zenodo.1098507 .

Published in JFM, 2014 by Avsarkisov, Oberlack & Hoyas. This study is seriously flawed. It also contains non-reproducible results. Details and corrections are given in https://arxiv.org/abs/1606.08396 ,  and in  https://arxiv.org/abs/2202.04635 (see Appendix C).

Published in Communications in Nonlinear Science and Numerical Simulation, 2011 by M. Oberlack. The explicit results in this study for the proposed filter functions are incorrect and need to be rederived. The problem throughout is that the developed filter functions are based on a pure 1D analysis, although LES filtering is a true 3D-process (for 3D turbulence). All integrals presented therein are therefore not 1D but have to be identified as 3D integrals, the coordinates $x$ and $k$, as well as the coordinate differences $x-y$, have to be identified as vector norms $|\mathbf{x}|$, $|\mathbf{k}|$, $|\mathbf{x}-\mathbf{y}|$, and usual products between coordinates as scalar products. Thus Eq.(7) has to be evaluated as a 3D Fourier-transform and not as a 1D Fourier-transform, as incorrectly done throughout this study. This will lead to different explicit results for the filter functions, even if they are assumed to be spherically symmetric — although this assumption of spher...