Инд. авторы:	Grebenev V.N., Wacławczyk M., Oberlack M.
Заглавие:	Conformal invariance of the Lungren-Monin-Novikov equations for vorticity fields in 2D turbulence
Библ. ссылка:	Grebenev V.N., Wacławczyk M., Oberlack M. Conformal invariance of the Lungren-Monin-Novikov equations for vorticity fields in 2D turbulence // Journal of Physics A: Mathematical and Theoretical. - 2017. - Vol.50. - Iss. 43. - Art.435502. - ISSN 1751-8113. - EISSN 1751-8121.
Внешние системы:	DOI: 10.1088/1751-8121/aa8c69; РИНЦ: 31082745; SCOPUS: 2-s2.0-85031008431; WoS: 000412212200002;
Реферат:	eng: We study the statistical properties of the vorticity field in two-dimensional turbulence. The field is described in terms of the infinite Lundgren-Monin-Novikov (LMN) chain of equations for multi-point probability density functions (pdf's) of vorticity. We perform a Lie group analysis of the first equation in this chain using the direct method based on the canonical Lie-Backlund transformations devised for integro-differential equations. We analytically show that the conformal group is broken for the first LMN equation i.e. for the 1-point pdf at least for the inviscid case but the equation is still conformally invariant on the associated characteristic with zero-vorticity. Then, we demonstrate that this characteristic is conformally transformed. We find this outcome coincides with the numerical results about the conformal invariance of the statistics of zero-vorticity isolines, see e.g. Falkovich (2007 Russian Math. Surv. 63 497-510). The conformal symmetry can be understood as a 'local scaling' and its traces in two-dimensional turbulence were already discussed in the literature, i.e. it was conjectured more than twenty years ago in Polyakov (1993 Nucl. Phys. B 396 367-85) and clearly validated experimentally in Bernard et al (2006 Nat. Phys. 2 124-8). © 2017 IOP Publishing Ltd.
Ключевые слова:	vorticity field; symmetry analysis; conformal invariance of zero-vorticity isolines; 2D turbulence; LundgrenMonin-Novikov chain of equations;
Издано:	2017
Физ. характеристика:	435502
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