Turbulence & Symmetries

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...

Published in Journal of Mathematical Physics, 2013 by Waclawczyk & Oberlack. This study is misleading and seriously flawed. Details and corrections are given in http://aip.scitation.org/doi/abs/10.1063/1.4940357   and more comprehensively in  https://doi.org/10.5281/zenodo.1101136 .

Published in Journal of Turbulence, 2013 by Oberlack & Zieleniewicz.  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  Discrete and Continuous Dynamical Systems, 2010 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 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 .

Published in  Combustion Theory and Modelling, 2001  by Oberlack, Wenzel & Peters. This publication is misleading and flawed. Although first correctly revealed as flawed by V.A. Sabel'nikov & A.N. Lipatnikov in https://doi.org/10.1260/1756-8277.2.4.301 , I want to lay open a further and even more fundamental problem of this study by Oberlack et al. which has been overlooked and not addressed so far: The generalized scaling symmetry (15a), or in its finite form (21a), is physically void, i.e., it cannot be exploited or used as a guideline for dynamical modelling, as it is misleadingly claimed in Section 3. The reason is that this symmetry does not participate in the dynamics of the flame surface. It is just an irrelevant relabelling symmetry without having any influence or impact on the dynamics of the $G$-equation. Sure, this symmetry defines the $G$-equation, as was shown in Section 2.3, but it has no consequences on the dynamics (i.e. on the solutions) of th...

Published in JFM, 1999 by M. Oberlack. This study is seriously flawed, including mathematical errors and conclusions that do not match results. All details and corrections are given in  https://arxiv.org/abs/1412.3069 . Although this Comment explicitly refers to only the subsequent but equally flawed study of M. Oberlack "A unified approach for symmetries in plane parallel turbulent shear flows" (JFM, 2001) , all discussions and corrections can be carried over one-to-one to this preceding 1999 release. The analysis in both publications is equivalent, except for a changed coordinate system: While the 2001 study uses planar coordinates, the 1999-study makes use of polar coordinates. The equivalence in the symmetry analysis is thus only modulo a coordinate transformation. In fact, the 2001-publication is the defining study for the 1999 release, which can also be easily seen when comparing the submission dates: The former was submitted to the journal two months earlier (7 ...

Published in JFM, 2001  by M. Oberlack. The key finding and conclusion of this publication is seriously misleading and flawed. Several technical mistakes were made in this study, including one analytical result that cannot even be reproduced. A detailed discussion can be found in  https://arxiv.org/abs/1412.3069 , and  https://arxiv.org/abs/2202.04635  (see Appendix D). They shed the correct light onto the method of Lie-group symmetry analysis when applied to the theory of turbulence. Because, as with any other analytical method, also the powerful and appealing Lie-group symmetry method cannot solve or circumvent the closure problem of turbulence as it is misleadingly and continually claimed by M. Oberlack. Although a complete list of all mistakes and their detailed discussion can be found in  https://arxiv.org/abs/1412.3069 , it may be of interest to summarize the key mistake here again:  The symmetry determining equations (3.12a)-(3.12c) are incor...

Inconsistent Data & Flawed Results The following publication by Avsarkisov, Oberlack & Hoyas (2021) is seriously flawed: New scaling laws for turbulent Poiseuille flow with wall transpiration – CORRIGENDUM https://doi.org/10.1017/jfm.2020.1174 Details and corrections are given in https://arxiv.org/abs/2202.04635 (see Appendix C)

Although this paper by Avsarkisov, Oberlack & Hoyas (JFM, 2021) is already a Corrigendum, it is still seriously flawed. Details and corrections to  https://doi.org/10.1017/jfm.2020.1174 are given in  https://arxiv.org/abs/2202.04635  (see Appendix C)

Misleading & Flawed Results The following publication by Oberlack, Hoyas, Kraheberger, Alcantara-Avila & Laux (2022) is seriously misleading and flawed: Turbulence statistics of arbitrary moments of wall-bounded shear flows: A symmetry approach  https://doi.org/10.1103/PhysRevLett.128.024502 Details and corrections are given in https://arxiv.org/abs/2202.04635 https://doi.org/10.5281/zenodo.4570586  

Misleading & Flawed Results The following publication by Waclawczyk, Grebenev & Oberlack (2021) is seriously misleading and flawed: Conformal invariance of the 1-point statistics of the zero-isolines of 2d scalar fields in inverse turbulent cascades https://doi.org/10.1103/PhysRevFluids.6.084610   Details and corrections are given in  https://arxiv.org/abs/2111.02822 https://doi.org/10.5281/zenodo.6228153

Misleading & Flawed Results The following publication by Grebenev, Waclawczyk & Oberlack (2021) is seriously misleading and flawed: Reply to Conformal invariance of the zero-vorticity Lagrangian path in 2D turbulence  https://doi.org/10.1088/1751-8121/abe49f Details and corrections are given in  https://arxiv.org/abs/2110.11057 https://doi.org/10.5281/zenodo.6228153

Misleading & Flawed Results The following publication by Grebenev, Waclawczyk & Oberlack (2021) is seriously misleading and flawed: Reply to Conformal invariance of the Lundgren-Monin-Novikov equations for vorticity fields in 2D turbulence  https://doi.org/10.1088/1751-8121/abe95b Details and corrections are given in  https://arxiv.org/abs/2110.11057 https://doi.org/10.5281/zenodo.6228153

Misleading Results The following publication by Sadeghi, Oberlack & Gauding (2021) is seriously misleading: New symmetry-induced scaling laws of passive scalar transport in turbulent plane jets https://doi.org/10.1017/jfm.2021.376   Details are given in  https://arxiv.org/abs/2202.04635 https://doi.org/10.5281/zenodo.4570586

Misleading & Flawed Results The following publication by Waclawczyk, Grebenev & Oberlack (2020) is misleading and flawed: Conformal invariance of characteristic lines in a class of hydrodynamic models  https://doi.org/10.3390/sym12091482 Details and corrections are given in  https://doi.org/10.5281/zenodo.6228153

Misleading & Flawed Results The following publication by Klingenberg, Oberlack & Pluemacher (2020) is misleading and flawed: Symmetries and turbulence modeling https://doi.org/10.1063/1.5141165 Details and corrections are given in https://arxiv.org/abs/2008.08580 https://doi.org/10.5281/zenodo.4275736

Misleading & Flawed Results The following publication by Grebenev, Waclawczyk & Oberlack (2019) is seriously misleading and flawed:  Conformal invariance of the zero-vorticity Lagrangian path in 2D turbulence https://doi.org/10.1088/1751-8121/ab2f61 Details and corrections are given in  https://doi.org/10.1088/1751-8121/abe49e https://arxiv.org/abs/2008.11715 https://arxiv.org/abs/2110.11057 https://doi.org/10.5281/zenodo.6228153

This paper by Oberlack, Hoyas, Kraheberger, Alcantara-Avila & Laux (Physical Review Letters, 2022) is seriously misleading and flawed. Details and corrections to https://doi.org/10.1103/PhysRevLett.128.024502 are given in https://arxiv.org/abs/2202.04635 https://doi.org/10.5281/zenodo.4570586  

This paper by Waclawczyk, Grebenev & Oberlack (Physical Review Fluids, 2021) is seriously misleading and flawed. Details and corrections to https://doi.org/10.1103/PhysRevFluids.6.084610 are given in  https://arxiv.org/abs/2111.02822 https://doi.org/10.5281/zenodo.6228153

This paper by Grebenev, Waclawczyk & Oberlack (Journal of Physics A, 2021) is seriously misleading and flawed. Details and corrections to https://doi.org/10.1088/1751-8121/abe49f are given in  https://arxiv.org/abs/2110.11057 https://doi.org/10.5281/zenodo.6228153

This paper by Grebenev, Waclawczyk & Oberlack (Journal of Physics A, 2021) is seriously misleading and flawed. Details and corrections to https://doi.org/10.1088/1751-8121/abe95b are given in  https://arxiv.org/abs/2110.11057 https://doi.org/10.5281/zenodo.6228153

This paper by Sadeghi, Oberlack & Gauding (JFM, 2021) is seriously misleading. Details to https://doi.org/10.1017/jfm.2021.376 are given in  https://arxiv.org/abs/2202.04635 https://doi.org/10.5281/zenodo.4570586

This paper by Waclawczyk, Grebenev & Oberlack (Symmetry, 2020) is misleading and flawed. Details and corrections to https://doi.org/10.3390/sym12091482 are given in  https://doi.org/10.5281/zenodo.6228153

This paper by Klingenberg, Oberlack & Pluemacher (Physics of Fluids, 2020) is misleading and flawed. Details and corrections to https://doi.org/10.1063/1.5141165 are given in https://arxiv.org/abs/2008.08580 https://doi.org/10.5281/zenodo.4275736

This paper by Grebenev, Waclawczyk & Oberlack (Journal of Physics A, 2019) is seriously misleading and flawed. Details and corrections to  https://doi.org/10.1088/1751-8121/ab2f61 are given in  https://doi.org/10.1088/1751-8121/abe49e https://arxiv.org/abs/2008.11715 https://arxiv.org/abs/2110.11057 https://doi.org/10.5281/zenodo.6228153

This paper by Klingenberg, Oberlack & Pluemacher (Springer Proceedings in Physics, 2019) is methodologically flawed and seriously misleading. Details and corrections to  https://doi.org/10.1007/978-3-030-22196-6_5 are given in https://publons.com/publon/27659704/#review-5598480 https://arxiv.org/abs/2008.08580 https://doi.org/10.5281/zenodo.4275736

This paper by Sadeghi, Oberlack & Gauding (JFM, 2018) is seriously flawed, including mathematical errors, inconsistent results and non-reproducible figures. Details and corrections to  https://doi.org/10.1017/jfm.2018.625 are given in https://doi.org/10.1017/jfm.2019.985 https://hal.archives-ouvertes.fr/hal-01888353 https://arxiv.org/abs/2202.04635  (see Section 3)

This paper by Dierkes & Oberlack (JFM, 2017) is misleading. Details to  https://doi.org/10.1017/jfm.2017.74 are given in https://publons.com/publon/877241/#review-820659

This paper by Hau, Oberlack & Chagelishvili (Journal of Mathematical Physics, 2017) is misleading and flawed. Details and corrections to https://doi.org/10.1063/1.4980055 are given in https://arxiv.org/abs/1712.03105 https://publons.com/publon/18162442/#review-4095661

This paper by Grebenev, Waclawczyk & Oberlack (Journal of Physics A, 2017) is misleading and flawed. Details and corrections to  https://doi.org/10.1088/1751-8121/aa8c69 are given in  https://doi.org/10.1088/1751-8121/abe95a https://arxiv.org/abs/1802.02490 https://arxiv.org/abs/2110.11057 https://doi.org/10.5281/zenodo.6228153

This paper by Waclawczyk, Grebenev & Oberlack (Journal of Physics A, 2017)  is misleading. Details to  https://doi.org/10.1088/1751-8121/aa62f4 are given in https://arxiv.org/abs/1710.00669

This paper by Waclawczyk & Oberlack (Journal of Physics, 2016) is seriously misleading and flawed, including mathematical errors and inconsistent conclusions. Details and corrections to  https://doi.org/10.1088/1742-6596/760/1/012038 are given in https://www.researchgate.net/publication/311285232

This paper by Waclawczyk, Janocha & Oberlack (Symmetry, 2016) is seriously misleading and flawed, including mathematical errors and inconsistent conclusions. Details and corrections to http://dx.doi.org/10.3390/sym8040024 are given in https://www.researchgate.net/publication/301553065

This paper by Waclawczyk & Oberlack (Journal of Mathematical Physics, 2016) is misleading and flawed, including mathematical errors and inconsistent conclusions. Details and corrections to http://aip.scitation.org/doi/abs/10.1063/1.4944424 are given in  https://www.researchgate.net/publication/299368809

This paper by Waclawczyk & Oberlack (Physical Review E, 2015) is misleading and flawed, including mathematical errors and inconsistent conclusions. Details and corrections to  https://doi.org/10.1103/PhysRevE.92.067002 are given in  https://www.researchgate.net/publication/287996194 https://arxiv.org/abs/1602.08039 https://arxiv.org/abs/1412.6949

This paper by Oberlack, Waclawczyk, Rosteck & Avsarkisov (Mechanical Engineering Reviews, 2015) is seriously misleading and flawed, including mathematical errors, inconsistent inferences, conclusions not matching results and non-reproducible figures. Details and corrections to  https://doi.org/10.1299/mer.15-00157 are given in https://doi.org/10.5281/zenodo.1101197 https://doi.org/10.5281/zenodo.1098507 https://doi.org/10.5281/zenodo.1101170 https://publons.com/publon/1636179/#review-1575480

This paper by Janocha, Waclawczyk & Oberlack (Symmetry, 2015)  is seriously flawed. Details and corrections to  http://dx.doi.org/10.3390/sym7031536 are given in http://dx.doi.org/10.3390/sym8040023 https://doi.org/10.5281/zenodo.1101170

This paper by Waclawczyk, Staffolani, Oberlack, Rosteck, Wilczek & Friedrich (Physical Review E, 2014)  is seriously misleading and flawed. Details and corrections to  https://doi.org/10.1103/PhysRevE.90.013022 are given in https://doi.org/10.1103/PhysRevE.92.067001 https://doi.org/10.5281/zenodo.1098507

This paper by Avsarkisov, Oberlack & Hoyas (JFM, 2014) is seriously flawed, including inconsistent results and non-reproducible figures. Details and corrections to  https://doi.org/10.1017/jfm.2014.98 are given in  https://arxiv.org/abs/1606.08396 https://arxiv.org/abs/2202.04635 (see Section 3 & Appendix C)

This paper by Waclawczyk & Oberlack (Journal of Mathematical Physics, 2013)  is misleading and flawed. Details and corrections to  http://aip.scitation.org/doi/abs/10.1063/1.4812803 are given in http://aip.scitation.org/doi/abs/10.1063/1.4940357 https://doi.org/10.5281/zenodo.1101136

This paper by Oberlack & Zieleniewicz (Journal of Turbulence, 2013)  is misleading. Details to http://www.tandfonline.com/doi/abs/10.1080/14685248.2012.759229 are given in https://arxiv.org/abs/1412.3061 https://doi.org/10.5281/zenodo.1101197

This paper by Oberlack & Rosteck (Discrete and Continuous Dynamical Systems, 2010) is seriously misleading.  Details to  http://aimsciences.org/article/doi/10.3934/dcdss.2010.3.451 are given in https://arxiv.org/abs/1412.3061 https://doi.org/10.5281/zenodo.1101197

This paper by Oberlack, Cabot, Pettersson-Reif & Weller (JFM, 2006) is misleading and flawed, including mathematical errors and inconsistent and non-reproducible conclusions. Details and corrections to  https://doi.org/10.1017/S0022112006001121 are given in  https://arxiv.org/abs/1609.08155

This paper by Oberlack, Wenzel & Peters  (Combustion Theory and Modelling, 2001)  is misleading and flawed. Details to http://www.tandfonline.com/doi/abs/10.1088/1364-7830/5/3/307 are given in http://journals.sagepub.com/doi/abs/10.1260/1756-8277.2.4.301 https://publons.com/publon/18141606/#review-4089011

This paper by Oberlack  (JFM, 1999)  is seriously flawed, including mathematical errors and conclusions that do not match results. Details and corrections to  https://doi.org/10.1017/S0022112098001542 are given in https://arxiv.org/abs/1412.3069

This paper by Oberlack  (JFM, 2001)  is seriously flawed, including mathematical errors and conclusions that do not match results. Details and corrections to  https://doi.org/10.1017/S0022112000002408  are given in https://arxiv.org/abs/1412.3069 https://arxiv.org/abs/2202.04635 (see Appendix D)

Methodologically Flawed & Seriously Misleading The following publication by Klingenberg, Oberlack & Pluemacher (2019) is methodologically flawed and seriously misleading: Symmetry-Based Turbulence Modeling https://doi.org/10.1007/978-3-030-22196-6_5 Details are given in the review  https://publons.com/publon/27659704/#review-5598480

Seriously Flawed, including Mathematical Errors, Inconsistent Results & Non-Reproducible Figures The following publication by Sadeghi, Oberlack & Gauding (2018) is flawed and non-reproducible: On new scaling laws in a temporally evolving turbulent plane jet using Lie symmetry analysis and direct numerical simulation https://doi.org/10.1017/jfm.2018.625 Details are given in  https://publons.com/publon/3075841/#review-3087670 and  https://www.researchgate.net/publication/328080340 The latter provides a full correction to Sadeghi et al. (2018). Note that JFM has the obscure policy not to publish any Comments on any of their articles.

Misleading & Flawed Results The following publication by Grebenev, Waclawczyk & Oberlack (2017) is flawed: Conformal invariance of the Lungren-Monin-Novikov equations for vorticity fields in 2D turbulence https://doi.org/10.1088/1751-8121/aa8c69 Details and corrections are given in  https://arxiv.org/abs/1802.02490

Misleading Results The following publication by Waclawczyk, Grebenev & Oberlack (2017) is misleading: Lie symmetry analysis of the Lundgren-Monin-Novikov equations for multi-point probability density functions of turbulent flow https://doi.org/10.1088/1751-8121/aa62f4 Details are given in  https://arxiv.org/abs/1710.00669

Seriously Misleading & Flawed, including Mathematical Errors & Inconsistent Conclusions The following publication by Waclawczyk & Oberlack (2016) is seriously flawed: Symmetry analysis and invariant solutions of the multipoint infinite systems describing turbulence https://doi.org/10.1088/1742-6596/760/1/012038 Details and corrections are given in  https://www.researchgate.net/publication/311285232

Seriously Misleading & Flawed, including Mathematical Errors & Inconsistent Conclusions The following publication by Waclawczyk, Janocha & Oberlack (2016) is seriously flawed: Reply to Frewer et al. Comments on Janocha et al. Lie Symmetry Analysis of the Hopf Functional-Differential Equation. Symmetry 2015, 7, 1536–1566 http://dx.doi.org/10.3390/sym8040024 Details and corrections are given in https://www.researchgate.net/publication/301553065

Misleading & Flawed, including Mathematical Errors & Inconsistent Conclusions The following publication by Waclawczyk & Oberlack (2016) is flawed: Response to “Comment on ‘Application of the extended Lie group analysis to the Hopf functional formulation of the Burgers equation’ ” [J. Math. Phys. 57, 034102 (2016)] http://aip.scitation.org/doi/abs/10.1063/1.4944424 Details and corrections are given in  https://www.researchgate.net/publication/299368809

Misleading & Flawed, including Mathematical Errors & Inconsistent Conclusions The following publication by Waclawczyk & Oberlack (2015) is flawed: Reply to “Comment on ‘Statistical symmetries of the Lundgren-Monin-Novikov hierarchy’ ” https://doi.org/10.1103/PhysRevE.92.067002 Details and corrections are given in  https://www.researchgate.net/publication/287996194 and  https://arxiv.org/abs/1602.08039 and  https://arxiv.org/abs/1412.6949

Seriously Misleading & Flawed, including Mathematical Errors & Inconsistent Inferences, as well as Conclusions not matching Results & Non-Reproducible Figures The following review by Oberlack, Waclawczyk, Rosteck & Avsarkisov (2015) is seriously flawed: Symmetries and their importance for statistical turbulence theory https://doi.org/10.1299/mer.15-00157 Details and corrections are given in  https://zenodo.org/record/1101198#.WlPROGeUhaQ and  https://zenodo.org/record/1204407#.WrFFaWrOVaQ and  https://zenodo.org/record/1204432#.WrFFvGrOVaQ Please also see the detailed Review  https://publons.com/publon/1636179/#review-1575480

Seriously Flawed, including Mathematical Errors & Inconsistent Results The following publication by Janocha, Waclawczyk & Oberlack (2015) is seriously flawed: Lie symmetry analysis of the Hopf functional-differential equation http://dx.doi.org/10.3390/sym7031536 Details and corrections are given in  http://dx.doi.org/10.3390/sym8040023 and more comprehensively in  https://zenodo.org/record/1204432#.WrE_HWrOVaQ

Seriously Misleading & Flawed The following publication by Waclawczyk, Staffolani, Oberlack, Rosteck, Wilczek & Friedrich (2014) is seriously misleading and flawed: Statistical symmetries of the Lundgren-Monin-Novikov hierarchy https://doi.org/10.1103/PhysRevE.90.013022 Details and corrections are given in  https://doi.org/10.1103/PhysRevE.92.067001 and more comprehensively in  https://zenodo.org/record/1204407#.WrFGJ2rOVaQ

Seriously Flawed, including Inconsistent Results and Non-Reproducible Figures The following JFM publication by Avsarkisov, Oberlack & Hoyas (2014) is flawed and non-reproducible: New scaling laws for turbulent Poiseuille flow with wall transpiration https://doi.org/10.1017/jfm.2014.98 Details and corrections are given in  https://arxiv.org/abs/1606.08396 Note that JFM has the obscure policy not to publish any Comments on any of their articles.

Misleading & Flawed The following publication by Waclawczyk & Oberlack (2013) is misleading and flawed: Application of the extended Lie group analysis to the Hopf functional formulation of the Burgers equation http://aip.scitation.org/doi/abs/10.1063/1.4812803 Details and corrections are given in  http://aip.scitation.org/doi/abs/10.1063/1.4940357 and more comprehensively in  https://zenodo.org/record/1204426#.WrFGdWrOVaQ

Misleading Results The following publication by Oberlack & Zieleniewicz (2013) is misleading: Statistical symmetries and its impact on new decay modes and integral invariants of decaying turbulence http://www.tandfonline.com/doi/abs/10.1080/14685248.2012.759229 Details are given in  https://arxiv.org/abs/1412.3061 and more comprehensively in  https://zenodo.org/record/1101198#.WlNejmeUhaQ

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

Misleading & Flawed: Mathematical Errors & Inconsistent and Non-Reproducible Conclusions The following JFM publication by Oberlack, Cabot, Pettersson-Reif & Weller (2006) is misleading and flawed, both numerically and analytically: Group analysis, direct numerical simulation and modelling of a turbulent channel flow with streamwise rotation https://doi.org/10.1017/S0022112006001121 Details and corrections are given in https://arxiv.org/abs/1609.08155 Note that JFM has the obscure policy not to publish any Comments on any of their articles.

Misleading Results The analytical result on the new third scaling group in the publication by Khujadze & Oberlack (2004) is misleading: DNS and scaling laws from new symmetry groups of ZPG turbulent boundary layer flow https://doi.org/10.1007/s00162-004-0149-x Details are given in  https://arxiv.org/abs/1412.3061 and more comprehensively in  https://zenodo.org/record/1101198#.WlNejmeUhaQ

Misleading & Flawed The following publication by Oberlack, Wenzel & Peters (2001) is misleading and flawed: On symmetries and averaging of the G-equation for premixed combustion http://www.tandfonline.com/doi/abs/10.1088/1364-7830/5/3/307 Details are given in  http://journals.sagepub.com/doi/abs/10.1260/1756-8277.2.4.301 See also the Review published at Publons:  https://publons.com/publon/18141606/#review-4089011

Seriously Flawed, including Mathematical Errors & Conclusions that do not match Results The following JFM publication by Oberlack (1999) is seriously flawed: Similarity in non-rotating and rotating turbulent pipe flows https://doi.org/10.1017/S0022112098001542 Details and corrections are given in the Comment  https://arxiv.org/abs/1412.3069 Note that JFM has the obscure policy not to publish any Comments on any of their articles.

Seriously Flawed, including Mathematical Errors & Conclusions that do not match Results The following JFM publication by Oberlack (2001) is seriously flawed: A unified approach for symmetries in plane parallel turbulent shear flows https://doi.org/10.1017/S0022112000002408 Details and corrections are given in the Comment  https://arxiv.org/abs/1412.3069 Note that JFM has the obscure policy not to publish any Comments on any of their articles.

https://doi.org/10.5281/zenodo.1101197 A detailed theoretical investigation is given which demonstrates that a recently proposed set of statistical symmetries is physically void. Although they are mathematically admitted as unique symmetry transformations by the underlying statistical Navier-Stokes equations up to the functional level of the Hopf equation, by closer inspection, however, they lead to physical inconsistencies and erroneous conclusions in the theory of turbulence. These new statistical symmetries are thus misleading in so far as they form within an unmodelled theory a set of analytical results which at the same time lacks physical consistency. Our investigation will expose this inconsistency on different levels of statistical description, where on each level we will gain new insights for their non-physical transformation behavior. With a view to generate invariant turbulent scaling laws, the consequences will be finally discussed when trying to analytically exploit su...

https://arxiv.org/abs/1412.3069 Essence of this Comment: Since the statistical equations in turbulence are unclosed, so are their symmetries. Hence, when performing any invariant analysis on such an unclosed system of equations, it will predominately result into a non-unique set of invariant solutions involving arbitrary functions for which from the outset it is not clear how to specify them.  The closure problem of turbulence cannot be circumvented, or “somewhat bypassed” in the sense of Oberlack  ➽ , by just employing the method of Lie-group invariant analysis alone, since the arbitrariness in the results just gets shifted from one function to another. Hence, without modelling these unclosed equations, an a priori prediction from Lie-group theory alone as how turbulence scales is and will not be possible. Only a posteriori, by anticipating what to expect from numerical or experimental data, the adequate invariant scalings can be generated through an iterative tri...

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.  ➽

https://doi.org/10.5281/zenodo.1101170 The above link is a collection of comments continuing a central comment by in Symmetry (2016):  Comments on Janocha et al.: Lie Symmetry Analysis of the Hopf Functional-Differential Equation

https://doi.org/10.5281/zenodo.1101136 The above link is a collection of comments continuing a central comment in J.Math.Phys. (2016):  Comment on “Application of the extended Lie group analysis to the Hopf functional formulation of the Burgers equation”

https://doi.org/10.5281/zenodo.1098507 The above link is a collection of comments continuing a central comment in Phys.Rev.E (2015):  Comment on “Statistical symmetries of the Lundgren-Monin-Novikov hierarchy” The latest comments on this issue are given in  https://arxiv.org/abs/1710.00669 https://www.researchgate.net/publication/311285232