SYMMETRIES OF THE LUNDGREN–MONIN–NOVIKOV EQUATION FOR PROBABILITY OF THE VORTICITY FIELD DISTRIBUTION

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Resumo

A.M. Polyakov suggested the programme to expand the symmetries admitted by hydrodynamic models to the conformal invariance of statistics in the inverse cascade where the conformal group is infinite-dimensional. In the present work, the group of transformations G of the \(n\)-point probability density function fn (PDF) is presented for the infinite chain of Lundgren–Monin–Novikov equations (the statistical form of the Euler equations) for vorticity fields of the two-dimensional inviscid flow. The problem is written in the Lagrangian setting. The main result is that the group G transforms conformally the zero-vorticity characteristics and invariantly a family of the fn-equations for PDF along these lines. The equations are not invariant along other characteristics. Moreover, the action of G conserves the class of PDF. The results obtained can be used for studying the invariance of statistical properties of the optical turbulence.

Sobre autores

V. Grebenev

Federal Research Center for Information and Computational Technologies

Autor responsável pela correspondência
Email: vngrebenev@gmail.com
Russia, Novosibirsk

A. Grishkov

Institute of Mathematics and Statistics, The University of Sao Paulo

Autor responsável pela correspondência
Email: grishkov@ime.usp.br
Brazil, Sao Paulo

M. Oberlack

Technical University of Darmstadt

Autor responsável pela correspondência
Email: oberlack@fdy.tu-darmstadt.de
Germany, Darmstadt

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Declaração de direitos autorais © В.Н. Гребенёв, А.Н. Гришков, М. Оберлак, 2023