A GAUGE-INVARIANT LAGRANGIAN DETERMINED BY THE n-POINT PROBABILITY DENSITY FUNCTION OF VORTICITY FIELD OF THE WAVE OPTICAL TURBULENCE

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Abstract

The geometry methods for Yang–Mills fields of the gauge transformations are applied to finding an invariant Lagrangian in fiber bundle of the configuration 2d space X of the turbulent flow defined by the n-point probability density function fn (PDF). The two-dimensional wave optical turbulence is considered in the case of the inverse cascade of energy. The n-point PDF of the vorticity field satisfies the fn-equation from the Landgren–Monin–Novikov (LMN) hierarchy. The basic result reads: we construct the Lagrangian which is invariant under a subgroup H⊂G – the group of the gauge transformations in fiber bundles of the space X and the conserved currents.

About the authors

V. N. Grebenev

Federal Research Center for Information and Computational Technologies

Author for correspondence.
Email: vngrebenev@gmail.com
Russia, Novosibirsk

A. N. Grishkov

Federal Research Center for Information and Computational Technologies

Author for correspondence.
Email: grishkov@ime.usp.br
Russia, Novosibirsk

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