Hydrodynamic Approximation for 2D Optical Turbulence: Statistical Distribution Symmetry

Optical turbulence is described in terms of multipoint probability density distribution functions (PDF) f n using the Lundgren–Monin–Novikov (LMN) equation (statistical form of the Euler equation) for the field of vortex w = ∇ × u in a 2D flow ( u is the weight velocity field). The evolution of Lagrangian particles occurs along the characteristics of the f n equation from the LMN hierarchy. The vorticity is preserved along the characteristics in the absence of an external random force. It is shown that the G group of conformal transformations invariantly transforms the characteristics of the equation with zero vorticity and the family of f n equations for PDF along these lines, or the statistics of zero-vorticity lines. Along other level lines w = const ≠ 0, the statistics is not conformally invariant. In addition, the action of G conserves the PDF class.