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

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–Novikov equation for vorticity itself. This fact, however, was explicitly proven in our paper in section 3.1 and even stated in the abstract. In our original publication (Grebenev et al 2017 J. Phys. A: Math. Theor. 50 435502) we showed that, if vorticity is rescaled by a factor which is a function of space x, equation governing its one-point probability density function is invariant when restricted to zero-vorticity. We would like to point out that Frewer and Khujadze systematically replace the infinitesimals derived in (Grebenev et al 2017 J. Phys. A: Math. Theor. 50 435502) by another operator claiming an alleged contradiction of our results with the normalisation condition. This, however, is fundamental mathematical error in Frewer and Khujadze.