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

VN Grebenev, M Wacławczyk… - Journal of Physics A …, 2019 - iopscience.iop.org
It was clearly validated experimentally in Bernard et al (2006 Nat. Phys. 2 124–8) that the
zero-vorticity isolines in 2D turbulence belong to the class of conformal invariant (Schram …

Conformal invariance of the 1-point statistics of the zero-isolines of scalar fields in inverse turbulent cascades

M Wacławczyk, VN Grebenev, M Oberlack - Physical Review Fluids, 2021 - APS
This study concerns conformal invariance of certain statistics in 2 d turbulence. Namely,
there exists numerical evidence by Bernard et al.[Nature Phys. 2, 124 (2006) 1745-2473 …

Conformal invariance of characteristic lines in a class of hydrodynamic models

M Wacławczyk, VN Grebenev, M Oberlack - Symmetry, 2020 - mdpi.com
This paper addresses the problem of the existence of conformal invariance in a class of
hydrodynamic models. For this we analyse an underlying transport equation for the one …

Lie symmetry analysis and conservation laws of the axially loaded Euler beam

L Xia, X Ge - Mathematics, 2022 - mdpi.com
By applying the Lie symmetry method, group-invariant solutions are constructed for axially
loaded Euler beams. The corresponding mathematical models of the beams are formulated …

Comment on 'Conformal invariance of the Lundgren–Monin–Novikov equations for vorticity fields in 2D turbulence'

M Frewer, G Khujadze - Journal of Physics A: Mathematical and …, 2021 - iopscience.iop.org
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 …

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

M Frewer, G Khujadze - arXiv preprint arXiv:2111.02822, 2021 - arxiv.org
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 …

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

M Frewer, G Khujadze - Journal of Physics A: Mathematical and …, 2021 - iopscience.iop.org
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 …

Symmetry transformations of the vortex field statistics in optical turbulence

VN Grebenev, AN Grishkov, SB Medvedev - Theoretical and Mathematical …, 2023 - Springer
We use the concept of gauge transformations in the proof of the invariance of the statistics of
zero-vorticity lines in the case of the inverse energy cascade in wave optical turbulence; we …

Reply to Comment on 'Conformal invariance of the Lundgren–Monin–Novikov equations for vorticity fields in 2D turbulence'

VN Grebenev, M Wacławczyk… - Journal of Physics A …, 2021 - iopscience.iop.org
We reject the recent criticism of Frewer and Khujadze completely. In their comment Frewer
and Khujadze demonstrate breaking of the conformal group by the 2D Lundgren–Monin …

SLE: differential invariants study

V Grebenev, A Grishkov - São Paulo Journal of Mathematical Sciences, 2022 - Springer
Random curves (produced by the Schramm–Loewner evolution SLE κ) of the fractal
dimension d κ= 1+ κ/8, κ< 8 given on a surface D⊂ R 3 and the conformal group (CG) that …