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60

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Education

December 2000 - December 2003

April 1995 - September 2000

## Publications

Publications (60)

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 o...

A fact-check is presented to a Webinar recently held at the Australasian Fluid Mechanics Society (AFMS) on symmetries and its applications in turbulence [M. Oberlack, Oct. 14th, 2020: https://www.afms.org.au/events.html]. More than a dozen of statements made therein prove to be misleading and partly even mathematically incorrect. No knowledge in Li...

This is an informal collection of comments, remarks and discussions which I received and which I had with various experts who interacted with my Fact-Check of the AFMS 2020-Webinar: “Symmetry induced turbulent scaling laws for arbitrary moments and their validation with DNS and experimental data”. This supplement will provide additional information...

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 t...

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...

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 a...

A brief fact-check is presented to a seminar [INI, 23rd March 2022] recently held by M. Oberlack on symmetries and its applications to turbulence. The seminar was part of the programme "Mathematical aspects of turbulence: where do we stand?", organised by the Isaac Newton Institute (INI). This fact-check will reveal important information that the s...

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), whic...

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), whic...

The current claim by Grebenev et al (2019 J. Phys. A: Math. Theor. 52 335501), 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 analysis published earlier by Grebenev et al (2017 J. Phys. A: Math. Theor. 50 435502). All results and co...

The recent claim by Grebenev et al (2017 J. Phys. A: Math. Theor. 50 435502) 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. To note is that within this comment t...

This comment provides a correction to the flawed and non-reproducible study by Sadeghi et al. (2018). By choosing a different but physically consistent set of equivalence transformations than the inconsistent one proposed by Sadeghi et al. (2018), it will be shown how for a temporally evolving plane jet the numerically computed statistical profiles...

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...

Every linear system of partial differential equations (PDEs) admits a scaling symmetry in its dependent variables. In conjunction with other admitted symmetries that only exhibit a linear dependence of the dependent variables in their infinitesimals, the associated differential condition to generate invariant solutions poses a linear eigenvalue pro...

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 rega...

Although knowing better due to numerous comments and discussions in the past two years, M. Oberlack and M. Waclawczyk continue to publish incorrect research results. This note helps to see why in a very illustrative form.

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 consen...

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...

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 v...

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 fa...

Despite correcting their symmetry analysis in Janocha et al. (2015) according to some of our comments put forward in Symmetry 8, 23 (2016), their revised method presented in Symmetry 8, 24 (2016) is still incorrect. In fact, even more strange and unrealistic symmetries are now obtained than before the correction. The key problem is that only second...

The recent systematic study by Janocha et al. [1] to determine all possible Lie-point symmetries for the functional Hopf-Burgers equation is re-examined. From a more consistent theoretical framework, however, some of the proposed symmetry transformations of the considered Hopf-Burgers equation are in fact rejected. Three out of eight proposed symme...

In the Response [J. Math. Phys. 57, 034103 (2016)] recently published to our Comment [J. Math. Phys. 57, 034102 (2016)], we will disclose a technical error which was not recognized during the peer-review process. This error has a far-reaching negative effect when trying to generate invariant solutions for the multi-point moments as proposed in thei...

The quest to find new statistical symmetries in the theory of turbulence is an ongoing research endeavor which is still in its beginning and exploratory stage. In our comment we show that the recently performed study of Wacławczyk and Oberlack [J. Math. Phys. 54, 072901 (2013)] failed to present such new statistical symmetries. Despite their existe...

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 example...

The published Reply [Phys.Rev. E 92, 067002 (2015)] of Oberlack et al. to our Comment [Phys.Rev. E 92, 067001 (2015)] contains a new but central reasoning error which unfortunately passed the peer-review process, a mistake which when corrected would lead to an overall opposite conclusion. This notification serves to correct the mistake and will giv...

To avoid a misconception of our Comment [Phys. Rev. E 92, 067001 (2015)], we want to explain our position in (I) “Violation of the causality principle” again. A misunderstanding can be based, for example, on the erroneous perception that we claim that Oberlack’s (et al.) PDF and multi-point correlation symmetries are not physical because they are n...

In the recently published Reply by Oberlack et al. [Phys. Rev. E 92, 067002 (2015)] an attempt is made to explain the notion of “statistical symmetry”. This 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...

The article by Oberlack et al. [Phys. Rev. E 90, 013022 (2014)] proposes two new statistical symmetries in the classical theory for turbulent hydrodynamic flows. In this Comment, however, we show that both symmetries are unphysical due to violating the principle of causality. In addition, they must get broken in order to be consistent with all phys...

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...

An instructive example is presented to elucidate the mathematical situation in the non-uniqueness problem of the infinite Friedmann-Keller hierarchy for all multi-point moments within the theory of spatially unbounded Navier-Stokes turbulence. It is shown that the non-uniqueness problem of the Friedmann-Keller hierarchy emerges from the property th...

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 brok...

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 equati...

Using the methodology of Lie groups and Lie algebras we determine new symmetry and equivalence classes of the stationary three-dimensional Euler equations by introducing potential functions that are based on the so-called dual stream function representation of the steady state velocity field u(x, y, z) = ∇λ(x, y, z) × ∇μ(x, y, z), which itself can...

Using the methodology of Lie groups and Lie algebras we determine new symmetry and equivalence classes of the stationary three-dimensional Euler equations by introducing potential functions that are based on the so-called dual stream function representation of the steady state velocity field u(x, y, z) = ∇λ(x, y, z) × ∇μ(x, y, z), which itself can...

This discussion consists of two parts. The first part introduces the neces-sary mathematical framework to construct invariant solutions from a global, and, if the underlying transformation acts as a Lie-group, also from a local perspective. This will be explicitly demonstrated in the frame of a 1-point and 2-point analysis, considering cer-tain spe...

A new, updated version is available: https://arxiv.org/abs/1611.07002

Based on the recent work by Frewer (2009), the central idea of modeling turbulence on a four-dimensional non-Riemannian manifold is extended herein to flow configurations which include solid walls as boundaries. Special focus is directed to rotating wall-bounded flows. The model development itself will be based on the strategy of closing the onepoi...

Without changing the physical content of the theory the statistical one-point Navier-Stokes equations are equivalently reformulated on a curved four-dimensional non-Riemannian manifold, with the result that the mean pressure gradient is automatically and consistently incorporated into the modelling scheme. This reformulation also natu-rally induces...

The aim of this new approach is to demonstrate that modelling on a 3D spatial manifold is not equivalent to modelling on a true 4D space-time manifold within Newtonian physics. In the framework of turbulence modelling it will be shown that by geometrically reformulating the averaged Navier-Stokes equations on a 4D non-Riemannian manifold without ch...

A new turbulence modelling approach is presented. Geometrically reformulating the averaged Navier–Stokes equations on a four-dimensional non-Riemannian manifold without changing the physical content of the theory, additional modelling restrictions which are absent in the usual Euclidean (3+1)-dimensional framework naturally emerge. The modelled equ...

Without changing the physical content the averaged Navier-Stokes equations are geometrically reformulated on a true 4D non-Riemannian space-time manifold. Its clear superiority over the usual (3+1)D Euclidean approach can be fully summarized as follows:
The variables of space and time are fully independent. This implies that in any closure strategy...

There was and still is a considerable amount of confusion in the community of classical continuum mechanics on the concept
of material frame-indifference. An extensive review is presented which will point out and try to resolve various misconceptions
that still accompany the literature of material frame-indifference. With the tools of differential...

When developing turbulence modelling from scratch certain questions arise which inevitably turn into methodological problems regarding this topic
What makes Euclidean transformations in classical continuum mechanics, in particular turbulence modelling, so special ?
Why is frame-dependency in all unclosed terms of existing algebraic models, e.g. in...

We discuss the incompressible stationary axisymmetric Euler equations with swirl, for which we derive via a scalar stream function an equivalent representation, the Bragg–Hawthorne equation [Bragg, S.L., Hawthorne, W.R., 1950. Some exact solutions of the flow through annular cascade actuator discs. J. Aero. Sci. 17, 243]. Despite this obvious equiv...

In the Hamiltonian light-cone approach to QCD an effective one-body equation for describing mesons with different quark and anti-quark flavor is broken down to an oversimplified model. This model serves as a platform to study explicit renormalization in a non-perturbative context. Two numerically and conceptually totally different renormalization s...

We apply the subtraction method to an effective QCD-inspired model, which includes the Coulomb plus a zero-range hyperfine interactions, to define a renormalized Hamiltonian for mesons. The spectrum of the renormalized Hamiltonian agrees with the one obtained with a smeared hyperfine interaction. The masses of the low-lying pseudoscalar and vector...

An ill-defined integral equation for modeling the mass-spectrum of mesons is regulated with an additional but unphysical parameter. This parameter dependance is removed by renormalization. Illustrative graphical examples are given.

We prove that lattice QCD generates the axial anomaly in the continuum limit under very general conditions on the lattice action, which includes the case of Ginsparg-Wilson fermions. The ingredients going into the proof are gauge invariance, locality of the Dirac operator, absence of fermion doubling, the general form of the lattice Ward identity,...

We prove that lattice QCD generates the axial anomaly in the continuum limit under very general conditions on the lattice action, which includes the case of Ginsparg-Wilson fermions. The ingredients going into the proof are gauge invariance, locality of the Dirac operator, absence of fermion doubling, the general form of the lattice Ward identity,...

## Projects

Projects (3)

Implementation of an open-source high-performance Fast Fourier Transform in multiprecision that can compete with non-free software as Mathematica and MATLAB, in both serial and parallel computations: https://github.com/mfrewer/mpFFT/

When applying Lie-group symmetry analysis to linear stability analysis, one has to be aware of the relative-motion aspect and the possibility to generate redundant modes even if they are group-theoretically inequivalent.

When applying Lie-group symmetry analysis to turbulent flows, one has to be aware of the all-embracing closure problem and the possibility to generate unphysical symmetries not matching empirical results: https://zenodo.org/communities/turbsym/