Symmetry transformations of the vortex field statistics in optical turbulence.

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 study it in the framework of the hydrodynamic approximation of the two-dimensional nonlinear Schrödinger equation for the weight velocity field . The multipoint probability distribution density functions of the vortex field satisfy an infinite chain of Lundgren–Monin–Novikov equations (statistical form of the Euler equations). The equations are considered in the case of the external action in the form of white Gaussian noise and large-scale friction, which makes the probability distribution density function statistically stationary. The main result is that the transformations are local and conformally transform the -point statistics of zero-vorticity lines or the probability that a random curve passes through points for , , where , is invariant under conformal transformations. [ABSTRACT FROM AUTHOR]