- PII
- 10.31857/S2686740023010054-1
- DOI
- 10.31857/S2686740023010054
- Publication type
- Status
- Published
- Authors
- Volume/ Edition
- Volume 509 / Issue number 1
- Pages
- 50-55
- Abstract
- 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.
- Keywords
- двумерная турбулентность уравнения Лангрена–Монина–Новикова конформная инвариантность линии нулевой завихренности
- Date of publication
- 16.09.2025
- Year of publication
- 2025
- Number of purchasers
- 0
- Views
- 13
References
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