二维turbulence中涡度场的共形不变性和Lundsl-Monin-Novikov方程：驳斥最近的一个主张
Conformal invariance and the Lundgren-Monin-Novikov equations for vorticity fields in 2D turbulence: Refuting a recent claim
摘要：
Grebenev等人[J. Phys. A：Math. Theor. 50，435502（2017）]，无粘二维Lundel-Monin-Novikov（LMN）方程在零涡度特征上自然会显示局部共形不变性，当仅通过经典李群对称方法分析这些时，是无效的，将在本评论中被驳斥。值得注意的是，在这篇评论中，2D湍流中（可能）存在共形不变性并没有受到质疑，只有Grebenev等人（2017）给出的结论以及他们如何推导出这种不变性的方法才是本文所批评和反驳的。事实上，Grebenev等人（2017）中二维LMN涡度方程的共形不变性的代数推导是有缺陷的。LMN方程的一个关键约束被错误地转换了。相反，提供正确的变换将导致破坏所宣称的共形群。Grebenev et al.（2017）的修正版本只是导致了场的全局恒定缩放，而不是声称的局部缩放。因此，由于在Grebenev等人（2017）中，只考虑了无限和未闭合LMN链中的第一个方程，因此这种校正也将导致单点和两点概率密度函数（PDF）的不同李群无穷小，从而取代所提出的误导性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
