George Khujadze | University of Siegen (original) (raw)

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Papers by George Khujadze

The current claim by Grebenev et al. [J. Phys. A: Math. Theor. 52, 335501 (2019)], namely that th... more 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.

The recent study by Klingenberg, Oberlack & Pluemacher (2020) proposes a new strategy for modelin... more 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.

The Lie-group-based symmetry analysis, as first proposed in Avsarkisov et al. (2014) and then lat... more 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, in that they violate the classical principle of cause and effect. In particular, as we consequently will show, the matching to the DNS data of the scalar dissipation, being a critical indicator to judge the prediction quality of any theoretically derived scaling law, fails exceedingly.

A better understanding of transition to turbulence in a Poiseuille flow rotating about the stream... more A better understanding of transition to turbulence in a Poiseuille flow rotating about the streamwise axis is sought by investigating the stability of the flow. Using the classical linear modal analysis, we define the instability envelop and find that the rotation increases the exponential growth of the most unstable mode and, for high levels of rotation, we observe a re-stabilization of the flow. The influence of rotation on transient energy growth is also investigated as the set of linear equations is non-normal. We show that the energetic growth can be of the order of O 10 3 in the sub-critical region but for high Ro the non-normality of the equation set is reduced, resulting in a decrease of the maximal energetic growth. The maximal growth is achieved by the purely spanwise disturbances until a certain point where the maximal energy growth is caused by oblique ones.

 Motivation and objectives  Flow geometry  Stochastic forcing and transient growth of perturba... more  Motivation and objectives  Flow geometry  Stochastic forcing and transient growth of perturbations  Model of near-wall weak forcing  DNS of the flow with the near-wall volume forcing  Results of turbulence control  Summary

We propose a new strategy of shear flow turbulence control which is realized by the imposition in... more We propose a new strategy of shear flow turbulence control which is realized by the imposition in the plane Cou-ette flow of a specially designed, non-symmetric in span-wise direction seed velocity perturbations by a near wall volume forcing. The configuration of the imposed perturba-tions ensures a gain of shear flow energy and the breaking of turbulence spanwise reflection symmetry – generates span-wise mean flow. The latter changes the self-sustained dy-namics of turbulence and results in considerable reduction of its level and kinetic energy production. It has to empha-sized that the generated spanwise mean flow is a result of the intrinsic, nonlinear processes in the forced turbulence and not directly introduced in the system. A model, near-wall weak forcing is designed to impose in the flow the per-turbations with required statistics and characteristics. The efficiency of the proposed scheme has been demonstrated by direct numerical simulation (DNS) using the plane Cou-ette fl...

The energy transient growth mechanism of linear perturbations in plane constant shear flows is re... more The energy transient growth mechanism of linear perturbations in plane constant shear flows is re-examined. Considering fluid particle dynamics and operating in terms of the pressure force, we focus on the physics of the energy exchange between the base flow and a single Kelvin mode (i.e. plane waves or spatial Fourier harmonics of perturbations). The keystone of the energy exchange physics is the elastic reflection of the fluid particles from the maximum pressure plane of the Kelvin mode. An interplay of these physics with the shear flow kinematics quantitatively exactly describes the transient growth and, what is most important, the linear dynamics of the system allows to construct the dynamical equations that are identical to the Euler ones. The proposed mechanism is equally applicable to two-and three-dimensional (2D and 3D) perturbations and, thus, shows the universal nature of the transient growth physics in contrast to the widely accepted explanations, separating 2D (Orr mech...

Springer Proceedings in Physics, 2014

Springer Proceedings in Physics, 2014

The sound generation by pure vortex mode disturbances in an two-dimensional (2D) unbounded invisc... more The sound generation by pure vortex mode disturbances in an two-dimensional (2D) unbounded inviscid plane Couette flow is investigated. We present results by Kelvin-mode analysis as well as numerical simulations of the Euler equations, while focusing on the dynamics in the spectral plane. Our results show a dominance of the anisotropic linear sound generation in subsonic shear flows by vortices inside the boundaries of rapid distortion theory (RDT). The linearly generated, highly directional field is comparable to the hydrodynamic field, which physical headstone is the mode coupling, induced by the nonnormality in shear flow systems at moderate shear rates of the velocity. Comparisons of the classical acoustic analogy (AA) approach by with the herein presented results identify the inability of AAs to capture the shear-induced anisotropy of the generated waves in the spectral plane.

Springer Proceedings in Physics, 2007

The current claim by Grebenev et al. [J. Phys. A: Math. Theor. 52, 335501 (2019)], namely that th... more 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.

The recent study by Klingenberg, Oberlack & Pluemacher (2020) proposes a new strategy for modelin... more 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.

The Lie-group-based symmetry analysis, as first proposed in Avsarkisov et al. (2014) and then lat... more 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, in that they violate the classical principle of cause and effect. In particular, as we consequently will show, the matching to the DNS data of the scalar dissipation, being a critical indicator to judge the prediction quality of any theoretically derived scaling law, fails exceedingly.

A better understanding of transition to turbulence in a Poiseuille flow rotating about the stream... more A better understanding of transition to turbulence in a Poiseuille flow rotating about the streamwise axis is sought by investigating the stability of the flow. Using the classical linear modal analysis, we define the instability envelop and find that the rotation increases the exponential growth of the most unstable mode and, for high levels of rotation, we observe a re-stabilization of the flow. The influence of rotation on transient energy growth is also investigated as the set of linear equations is non-normal. We show that the energetic growth can be of the order of O 10 3 in the sub-critical region but for high Ro the non-normality of the equation set is reduced, resulting in a decrease of the maximal energetic growth. The maximal growth is achieved by the purely spanwise disturbances until a certain point where the maximal energy growth is caused by oblique ones.

 Motivation and objectives  Flow geometry  Stochastic forcing and transient growth of perturba... more  Motivation and objectives  Flow geometry  Stochastic forcing and transient growth of perturbations  Model of near-wall weak forcing  DNS of the flow with the near-wall volume forcing  Results of turbulence control  Summary

We propose a new strategy of shear flow turbulence control which is realized by the imposition in... more We propose a new strategy of shear flow turbulence control which is realized by the imposition in the plane Cou-ette flow of a specially designed, non-symmetric in span-wise direction seed velocity perturbations by a near wall volume forcing. The configuration of the imposed perturba-tions ensures a gain of shear flow energy and the breaking of turbulence spanwise reflection symmetry – generates span-wise mean flow. The latter changes the self-sustained dy-namics of turbulence and results in considerable reduction of its level and kinetic energy production. It has to empha-sized that the generated spanwise mean flow is a result of the intrinsic, nonlinear processes in the forced turbulence and not directly introduced in the system. A model, near-wall weak forcing is designed to impose in the flow the per-turbations with required statistics and characteristics. The efficiency of the proposed scheme has been demonstrated by direct numerical simulation (DNS) using the plane Cou-ette fl...

The energy transient growth mechanism of linear perturbations in plane constant shear flows is re... more The energy transient growth mechanism of linear perturbations in plane constant shear flows is re-examined. Considering fluid particle dynamics and operating in terms of the pressure force, we focus on the physics of the energy exchange between the base flow and a single Kelvin mode (i.e. plane waves or spatial Fourier harmonics of perturbations). The keystone of the energy exchange physics is the elastic reflection of the fluid particles from the maximum pressure plane of the Kelvin mode. An interplay of these physics with the shear flow kinematics quantitatively exactly describes the transient growth and, what is most important, the linear dynamics of the system allows to construct the dynamical equations that are identical to the Euler ones. The proposed mechanism is equally applicable to two-and three-dimensional (2D and 3D) perturbations and, thus, shows the universal nature of the transient growth physics in contrast to the widely accepted explanations, separating 2D (Orr mech...

Springer Proceedings in Physics, 2014

Springer Proceedings in Physics, 2014

The sound generation by pure vortex mode disturbances in an two-dimensional (2D) unbounded invisc... more The sound generation by pure vortex mode disturbances in an two-dimensional (2D) unbounded inviscid plane Couette flow is investigated. We present results by Kelvin-mode analysis as well as numerical simulations of the Euler equations, while focusing on the dynamics in the spectral plane. Our results show a dominance of the anisotropic linear sound generation in subsonic shear flows by vortices inside the boundaries of rapid distortion theory (RDT). The linearly generated, highly directional field is comparable to the hydrodynamic field, which physical headstone is the mode coupling, induced by the nonnormality in shear flow systems at moderate shear rates of the velocity. Comparisons of the classical acoustic analogy (AA) approach by with the herein presented results identify the inability of AAs to capture the shear-induced anisotropy of the generated waves in the spectral plane.

Springer Proceedings in Physics, 2007