arXiv subjects

Michael Frewer

Publications and source records attributed to Michael Frewer.

At least 19 recordsLinked to original sources

arXiv2023

An example from turbulence how not to use the invariant function method of Lie-group symmetries

The recent Reply by Oberlack et al. [Phys. Rev. Lett. 130, 069403 (2023)] fails to rebut the critique that a mathematical solution method has been misapplied in their original work. On a point-by-point basis we prove that all arguments put forward in that Reply are incorrect. Therefore, the fact that the invariant solution method of Lie-group symmetries should not be used for unclosed systems in the same way as for closed systems still holds true. Ignoring this fact only leads to wrong conclusions. Claims such as having derived solutions of the statistical Navier-Stokes equations from first principles, or having found a measure for the intermittent behaviour of turbulence or particularly the true scaling in wall-bounded turbulent shear flows, are incorrect.

physics.flu-dyn↗

arXiv2022

No new scaling laws of passive scalar with a constant mean gradient in decaying isotropic turbulence

In the study by Sadeghi & Oberlack [JFM 899, A10 (2020)] it is claimed that new scaling laws are derived for the case of passive scalar dynamics under the influence of a constant mean gradient in decaying homogeneous isotropic turbulence. However, these scaling laws are not new and have already been derived and discussed in Bahri (2016). No novel analytical achievements are made by Sadeghi & Oberlack, as the title of their study misleadingly wants to suggest. In fact, the already established self-similar scaling laws obtained by Bahri through simple dimensional analysis are already more general in the application than the ones obtained by Sadeghi & Oberlack through an overly complicated and therefore unnecessarily performed Lie-group symmetry analysis. The claim that it has the virtue of not being an ad-hoc method is not true. Because, instead of using an a priori set of scales as the classical method, the Lie-group method has to make use of an a priori set of symmetries, namely to select the correct relevant symmetries from an infinite and thus unclosed set. For example, a nonphysical scaling symmetry is selected which in the course of the analysis has to be discarded since it is not compatible with the data simulated. Hence, the Lie-group symmetry method in turbulence is just another common trial-and-error method and not a first-principle method that can bypass the closure problem.

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arXiv2022

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

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.

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arXiv2021

A critical examination of the conformal invariance in the statistical equations of 2D turbulent scalar fields

The recent study by Waclawczyk et al. [Phys. Rev. Fluids 6, 084610 (2021)] on conformal invariance in 2D turbulence is misleading as it makes three incorrect claims that form the core of their work. We will correct these claims and put them into the right perspective: First, the conformal invariance as proposed by Waclawczyk et al. is not related to the result that zero-isolines of the scalar field in the inverse energy cascade display a Schramm-Loewner evolution (SLE). Second, the conformal invariance is not a Lie-group for all values of the scalar field since it inherently violates the smoothness axiom of a Lie-group action, with the effect that a physical PDF gets mapped to a non-physical one. Third, although Waclawczyk et al. recognize that their conformal invariance does not constitute a symmetry but only a weaker equivalence transformation, it is still not classified correctly. The claim that their equivalence can map between solutions is not true. This fact will be demonstrated by using an illustrative example.

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arXiv2021

Refuting the claim of conformal invariance for a zero-vorticity characteristic equation in 2D turbulence

Although the current Reply by Grebenev et al. (2021a) makes their original analysis in Grebenev et al. (2017) more transparent, the actual problem remains. Their claim to have analytically proven conformal invariance in 2D turbulence for a zero-vorticity characteristic equation is not true. We refuted this claim in Frewer & Khujadze (2021a,b), which we will briefly summarize here again with respect to the presented Reply. In particular our proof on the symmetry-breaking property of the integral normalization constraint is misrepresented and misconstrued, especially in their second Reply (Grebenev et al., 2021b). Although the journal's only selected expert reviewer clearly agreed with our proof in his final conclusion, the journal nevertheless decided to publish the Replies.

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arXiv2020

Symmetries and turbulence modeling. A critical examination

The recent study by Klingenberg, Oberlack & Pluemacher (2020) proposes a new strategy for modeling turbulence in general. A proof-of-concept is presented therein for the particular flow configuration of a spatially evolving turbulent planar jet flow, coming to the conclusion that their model can generate scaling laws which go beyond the classical ones. Our comment, however, shows that their proof-of-concept is flawed and that their newly proposed scaling laws do not go beyond any classical solutions. Hence, their argument of having established a new and more advanced turbulence model cannot be confirmed. The problem is already rooted in the modeling strategy itself, in that a nonphysical statistical scaling symmetry gets implemented. Breaking this symmetry will restore the internal consistency and will turn all self-similar solutions back to the classical ones. To note is that their model also includes a second nonphysical symmetry. One of the authors already acknowledged this fact for turbulent jet flow in a formerly published Corrigendum (Sadeghi, Oberlack & Gauding, 2020). However, the Corrigendum is not cited and so the reader is not made aware that their method has fundamental problems that lead to inconsistencies and conflicting results. Instead, the very same nonphysical symmetry gets published again. Yet, this unscientific behaviour is not corrected, but repeated and continued in the subsequent and further misleading publication Klingenberg & Oberlack (2022), which is examined in this update in the appendix.

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arXiv2020

Comment on 'Conformal invariance of the zero-vorticity Lagrangian path in 2D turbulence'

The current claim by Grebenev et al. [J. Phys. A: Math. Theor. 52, 335501 (2019)], namely that the inviscid and unclosed 2D Lundgren-Monin-Novikov (LMN) equations on a zero-vorticity Lagrangian path admit conformal invariance, is based on a flawed and misleading analysis published earlier by Grebenev et al. (2017). All false results and conclusions made before in the Eulerian picture were now extended by Grebenev et al. (2019) to the Lagrangian picture. Although we have already commented on these errors and consistently refuted their previous study (Frewer & Khujadze, 2018), we deem it necessary to address and discuss these errors again in the new formulation and notation of Grebenev et al. (2019) as it will offer new insights into this issue.

physics.flu-dyn↗

arXiv2020

Conformal invariance and the Lundgren-Monin-Novikov equations for vorticity fields in 2D turbulence: Refuting a recent claim

The recent claim by Grebenev et al. [J. Phys. A: Math. Theor. 50, 435502 (2017)] that the inviscid 2D Lundgren-Monin-Novikov (LMN) equations on a zero vorticity characteristic naturally would reveal local conformal invariance when only analyzing these by means of a classical Lie-group symmetry approach, is invalid and will be refuted in the present comment. To note is that within this comment the (possible) existence of conformal invariance in 2D turbulence is not questioned, only the conclusion as is given in Grebenev et al. (2017) and their approach how this invariance was derived is what is being criticized and refuted herein. In fact, the algebraic derivation for conformal invariance of the 2D LMN vorticity equations in Grebenev et al. (2017) is flawed. A key constraint of the LMN equations has been wrongly transformed. Providing the correct transformation instead will lead to a breaking of the proclaimed conformal group. The corrected version of Grebenev et al. (2017) just leads to a globally constant scaling in the fields and not to a local one as claimed. In consequence, since in Grebenev et al. (2017) only the first equation within the infinite and unclosed LMN chain is considered, also different Lie-group infinitesimals for the one- and two-point probability density functions (PDFs) will result from this correction, replacing thus the misleading ones proposed.

physics.flu-dyn↗

arXiv2017

On physically redundant and irrelevant features when applying Lie-group symmetry analysis to hydrodynamic stability analysis

Every linear system of partial differential equations (PDEs) admits a scaling symmetry in its dependent variables. In conjunction with other admitted symmetries of linear type, the associated invariant solution condition poses a linear eigenvalue problem. If this problem is structured such that the spectral theorem applies, then the general solution of the considered linear PDE system is obtained by summing or integrating the invariant eigenfunctions (modes) over all eigenvalues, depending on whether the spectrum of the operator is discrete or continuous. By first studying the 1-D diffusion equation as a demonstrating example, this method is then applied to a relevant 2-D problem from hydrodynamic stability analysis. The aim of this study is to draw attention to the following two independent facts that need to be addressed in future studies when constructing solutions for linear PDEs with the method of Lie-symmetries: (i) Although each new symmetry leads to a mathematically different spectral decomposition, they may all be physically redundant to standard ones and do not reveal a new physical mechanism behind the overall considered dynamical process, as incorrectly asserted, for example, in the recent studies by the group of Oberlack et al. Hence, with regard to linear stability analysis, no physically "new" or more "general" modes are generated by this method than the ones already established. (ii) Next to the eigenvalue parameters, each single mode can also acquire non-system parameters, depending on the choice of its underlying symmetry. These symmetry-induced parameters, however, are all physically irrelevant, since their effect on a single mode will cancel when considering all modes collectively. In particular, the collective action of all single modes is identical for all symmetry-based decompositions and thus indistinguishable when considering the full physical fields.

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arXiv2017

Comment on 'Lie symmetry analysis of the Lundgren-Monin-Novikov equations for multi-point probability density functions of turbulent flow'

The recent study by Waclawczyk et al. [J. Phys. A: Math. Theor. 50, 175501 (2017)] possesses three shortcomings: (i) The analysis misses a key aspect of the LMN equations which makes their Lie-group symmetry results incomplete. In particular, two essential symmetries will break when including this aspect. (ii) The statements on the constraints regarding the infinite-dimensional symmetry groups are misleading. (iii) The particular symmetries originating solely from the linearity of the LMN hierarchy violate the classical principle of cause and effect and therefore are unphysical. Within this Comment we present a detailed proof to this claim and conclude with the note that the new study by Waclawczyk et al. gives an unrealistic outlook on deriving invariant symmetry solutions for velocity correlations that arise from intermittent processes.

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arXiv2016

Covariance and objectivity in mechanics and turbulence

Form-invariance (covariance) and frame-indifference (objectivity) are two notions in classical continuum mechanics which have attracted much attention and controversy over the past decades. Particularly in turbulence modelling it seems that there still is a need for clarification. The aim and purpose of this study is fourfold: (i) To achieve consensus in general on definitions and principles when trying to establish an invariant theory for modelling constitutive structures and dynamic processes in mechanics, where special focus is put on the principle of Material Frame-Indifference (MFI). (ii) To show that in constitutive modelling MFI can only be regarded as an approximation that needs to be reduced to a weaker statement when trying to advance it to an axiom of nature. (iii) To convince that in dynamical modelling, as in turbulence, MFI may not be utilized as a modelling guideline, not even in an approximative sense. Instead, its reduced form has to be supplemented by a second, independent axiom that includes the microscopic (fluctuating) description of the dynamical processes. Concerning Navier-Stokes turbulence, the axiom of Turbulent Frame-Indifference (TFI) is stated in which turbulence has to be modelled consistently with the invariant properties of the deterministic Navier-Stokes equations, and finally (iv) to propose a novel invariant modelling ansatz both for constitutive and dynamical modelling that allows to include the (mean) velocity field as an own independent modelling variable, however, not in an absolute but only in the relative sense as a velocity difference; a result that would systematically improve current modelling procedures in extended thermodynamics and turbulence theory to be more consistent with physical observations.

math-ph↗

arXiv2016

On the physical inconsistency of a new statistical scaling symmetry in incompressible Navier-Stokes turbulence

A detailed theoretical investigation is given which demonstrates that a recently proposed statistical scaling symmetry is physically void. Although this scaling is mathematically admitted as a unique symmetry transformation by the underlying statistical equations for incompressible Navier-Stokes turbulence on the level of the functional Hopf equation, by closer inspection, however, it leads to physical inconsistencies and erroneous conclusions in the theory of turbulence. The new statistical symmetry is thus misleading in so far as it forms within an unmodelled theory an analytical result 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 its non-physical transformation behavior. With a view to generate invariant turbulent scaling laws, the consequences will be finally discussed when trying to analytically exploit such a symmetry. In fact, a mismatch between theory and numerical experiment is conclusively quantified. We ultimately propose a general strategy on how to not only track unphysical statistical symmetries, but also on how to avoid generating such misleading invariance results from the outset. All the more so as this specific study on a physically inconsistent scaling symmetry only serves as a representative example within the broader context of statistical invariance analysis. In this sense our investigation is applicable to all areas of statistical physics in which symmetries get determined in order to either characterize complex dynamical systems, or in order to extract physically useful and meaningful information from the underlying dynamical process itself.

physics.flu-dyn↗

arXiv2016

A critical examination of the statistical symmetries admitted by the Lundgren-Monin-Novikov hierarchy of unconfined turbulence

We present a critical examination of the recent article by Waclawczyk et al. (2014) which proposes two new statistical symmetries in the classical theory for turbulent hydrodynamic flows. We first show that both symmetries are unphysical in that they induce inconsistencies due to violating the principle of causality. In addition, they must get broken in order to be consistent with all physical constraints naturally arising in the statistical Lundgren-Monin-Novikov (LMN) description of turbulence. As a result, we state that besides the well-known classical symmetries of the LMN equations no new statistical symmetries exist. Yet, aside from this particular issue, the article by Waclawczyk et al. (2014) is flawed in more than one respect, ranging from an incomplete proof, to a self-contradicting statement up to an incorrect claim. All these aspects will be listed, discussed and corrected, thus obtaining a completely opposite conclusion in our study than the article by Waclawczyk et al. (2014) is proposing.

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arXiv2016

On the use of applying Lie-group symmetry analysis to turbulent channel flow with streamwise rotation

The study by Oberlack et al. (2006) consists of two main parts: a direct numerical simulation (DNS) of a turbulent plane channel flow with streamwise rotation and a preceding Lie-group symmetry analysis on the two-point correlation equation (TPC) to analytically predict the scaling of the mean velocity profiles for different rotation rates. We will only comment on the latter part, since the DNS result obtained in the former part has already been commented on by Recktenwald et al. (2009), stating that the observed mismatch between DNS and their performed experiment is possibly due to the prescription of periodic boundary conditions on a too small computational domain in the spanwise direction. By revisiting the group analysis part in Oberlack et al. (2006), we will generate more natural scaling laws describing better the mean velocity profiles than the ones proposed. However, due to the statistical closure problem of turbulence, this improvement is illusive. As we will demonstrate, any arbitrary invariant scaling law for the mean velocity profiles can be generated consistent to any higher order in the velocity correlations. This problem of arbitrariness in invariant scaling persists even if we would formally consider the infinite statistical hierarchy of all multi-point correlation equations. The closure problem of turbulence simply cannot be circumvented by just employing the method of Lie-group symmetry analysis alone: as the statistical equations are unclosed, so are their symmetries! Hence, an a priori prediction as how turbulence scales is thus not possible. Only a posteriori by anticipating what to expect from numerical or experimental data the adequate invariant scaling law can be generated through an iterative trial-and-error process. Finally, apart from this issue, also several inconsistencies and incorrect statements to be found in Oberlack et al. (2006) will be pointed out.

physics.flu-dyn↗

arXiv2016

Revisiting the Lie-group symmetry method for turbulent channel flow with wall transpiration

The Lie-group-based symmetry analysis, as first proposed in Avsarkisov et al. (2014) and then later modified in Oberlack et al. (2015), to generate invariant solutions in order to predict the scaling behavior of a channel flow with uniform wall transpiration, is revisited. By focusing first on the results obtained in Avsarkisov et al. (2014), we failed to reproduce two key results: (i) For different transpiration rates at a constant Reynolds number, the mean velocity profiles (in deficit form) do not universally collapse onto a single curve as claimed. (ii) The universally proposed logarithmic scaling law in the center of the channel does not match the direct numerical simulation (DNS) data for the presented parameter values. In fact, no universal scaling behavior in the center of the channel can be detected from their DNS data, as it is misleadingly claimed in Avsarkisov et al. (2014). Moreover, we will demonstrate that the assumption of a Reynolds-number independent symmetry analysis is not justified for the flow conditions considered therein. Only when including also the viscous terms, an overall consistent symmetry analysis can be provided. This has been attempted in their subsequent study Oberlack et al. (2015). But, also the (viscous) Lie-group-based scaling theory proposed therein is inconsistent, apart from the additional fact that this study of Oberlack et al. (2015) is also technically flawed. The reason for this permanent inconsistency is that their symmetry analysis constantly involves several unphysical statistical symmetries that are incompatible to the underlying deterministic description of Navier-Stokes turbulence.

physics.flu-dyn↗

arXiv2016

Is the log-law a first principle result from Lie-group invariance analysis?

The invariance method of Lie-groups in the theory of turbulence carries the high expectation of being a first principle method for generating statistical scaling laws. The purpose of this comment is to show that this expectation has not been met so far. In particular for wall-bounded turbulent flows, the prospects for success are not promising in view of the facts we will present herein. Although the invariance method of Lie-groups is able to generate statistical scaling laws for wall-bounded turbulent flows, like the log-law for example, these invariant results yet not only fail to fulfil the basic requirements for a first principle result, but also are strongly misleading. The reason is that not the functional structure of the log-law itself is misleading, but that its invariant Lie-group based derivation yielding this function is what is misleading. By revisiting the study of Oberlack (2001) we will demonstrate that all Lie-group generated scaling laws derived therein do not convince as first principle solutions. Instead, a rigorous derivation reveals complete arbitrariness rather than uniqueness in the construction of invariant turbulent scaling laws. Important to note here is that the key results obtained in Oberlack (2001) are based on several technical errors, which all will be revealed, discussed and corrected. The reason and motivation why we put our focus solely on Oberlack (2001) is that it still marks the core study and central reference point when applying the method of Lie-groups to turbulence theory. Hence it is necessary to shed the correct light onto that study. Nevertheless, even if the method of Lie-groups in its full extent is applied and interpreted correctly, strong natural limits of this method within the theory of turbulence exist, which, as will be finally discussed, constitute insurmountable obstacles in the progress of achieving a significant breakthrough.

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arXiv2016

A note on the notion "statistical symmetry"

A critical review is presented on the most recent attempt to generally explain the notion of "statistical symmetry". This particular explanation, however, is incomplete and misses one important and essential aspect. The aim of this short note is to provide this missing information and to clarify this notion on the basis of a few instructive examples.

physics.flu-dyn↗

arXiv2015

Application of Lie-group symmetry analysis to an infinite hierarchy of differential equations at the example of first order ODEs

This study will explicitly demonstrate by example that an unrestricted infinite and forward recursive hierarchy of differential equations must be identified as an unclosed system of equations, despite the fact that to each unknown function in the hierarchy there exists a corresponding determined equation to which it can be bijectively mapped to. As a direct consequence, its admitted set of symmetry transformations must be identified as a weaker set of indeterminate equivalence transformations. The reason is that no unique general solution can be constructed, not even in principle. Instead, infinitely many disjoint and thus independent general solution manifolds exist. This is in clear contrast to a closed system of differential equations that only allows for a single and thus unique general solution manifold, which, by definition, covers all possible particular solutions this system can admit. Herein, different first order Riccati-ODEs serve as an example, but this analysis is not restricted to them. All conclusions drawn in this study will translate to any first order or higher order ODEs as well as to any PDEs.

math-ph↗