TY - JOUR

T1 - Hydrodynamic Approximation for 2D Optical Turbulence: Statistical Distribution Symmetry

AU - Grebenev, V. N.

AU - Grishkov, A. N.

AU - Medvedev, S. B.

AU - Fedoruk, M. P.

N1 - This study was supported by the Russian Science Foundation (project no. 22-11-00287). The work by A.N. Grishkov was supported by FAPESP (Brazil) (project no. 2021/09845-0).

PY - 2023/9

Y1 - 2023/9

N2 - Optical turbulence is described in terms of multipoint probability density distribution functions (PDF) fn 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 fn 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 fn 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.

AB - Optical turbulence is described in terms of multipoint probability density distribution functions (PDF) fn 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 fn 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 fn 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.

KW - 2D Schrödinger equation

KW - Lundgren–Monin–Novikov equations

KW - conformal invariance

KW - zero-vorticity lines

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85169889470&origin=inward&txGid=d0cf1f69ea1525fd3f1f977d84cf904e

UR - https://www.mendeley.com/catalogue/c214b3b8-c3c4-3f38-b3a6-88ecf1782115/

U2 - 10.3103/S106833562315006X

DO - 10.3103/S106833562315006X

M3 - Article

VL - 50

SP - S343-S354

JO - Bulletin of the Lebedev Physics Institute

JF - Bulletin of the Lebedev Physics Institute

SN - 1068-3356

ER -