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

The comment by Frewer and Khujadze contains fundamental mathematical errors and must therefore be rejected in its entirety. In Grebenev et al (2019 J. Phys. A: Math. Theor. 52 335501) conformal invariance of the zero-vorticity characteristics of the first equation from the Lundgren-Monin-Novikov (LMN) hierarchy for vorticity in 2D was addressed. On the contrary, Frewer and Khujadze consider the first LMN equation itself. In such a case the conformal group is broken, which was clearly stated in our above paper. This makes it clear that all conclusions in Frewer and Khujadze are completely wrong. We would like to point out that Frewer and Khujadze systematically replace the infinitesimals we derived by another form given by [equation (5) in the comment], aiming to prove semblance of inconsistency of our results with the normalisation constraint. We show that, for transformations derived in our paper, the invariance of this constraint follows straightforwardly.

Automated summary

The comment by Frewer and Khujadze is rejected due to fundamental mathematical errors, as Grebenev et al discussed the conformal invariance of zero-vorticity characteristics in the 2D vorticity equation. Frewer and Khujadze attempted to show inconsistency with the normalization constraint by replacing the infinitesimals derived by others. In reality, the invariance of this constraint follows straightforwardly in the transformations derived in the paper.