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Hydrodynamic Approximation for 2D Optical Turbulence: Statistical Distribution Symmetry

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Abstract

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.

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ACKNOWLEDGMENTS

The authors are grateful to Prof. M. Wacławczyk for fruitful discussions of this work.

Funding

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).

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Authors and Affiliations

  1. Federal Research Center of Information and Computational Technologies, 630090, Novosibirsk, Russia

    V. N. Grebenev & S. B. Medvedev

  2. Institute of Mathematics and Statistics, University of São Paulo, São Paulo, Brasil

    A. N. Grishkov

  3. Novosibirsk National Research State University, 630090, Novosibirsk, Russia

    M. P. Fedoruk

Authors
  1. V. N. Grebenev
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  2. A. N. Grishkov
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  3. S. B. Medvedev
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  4. M. P. Fedoruk
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Corresponding author

Correspondence to V. N. Grebenev.

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Translated by N. Wadhwa

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Grebenev, V.N., Grishkov, A.N., Medvedev, S.B. et al. Hydrodynamic Approximation for 2D Optical Turbulence: Statistical Distribution Symmetry. Bull. Lebedev Phys. Inst. 50 (Suppl 3), S343–S354 (2023). https://doi.org/10.3103/S106833562315006X

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  • DOI: https://doi.org/10.3103/S106833562315006X

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