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Conformal invariance of the Lungren–Monin–Novikov equations for vorticity fields in 2D turbulence

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dc.abstract.enWe 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-Bäcklund 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).
dc.affiliationUniwersytet Warszawski
dc.contributor.authorWacławczyk, Marta
dc.contributor.authorGrebenev, Vladimir
dc.contributor.authorOberlack, M.
dc.date.accessioned2024-01-24T20:06:10Z
dc.date.available2024-01-24T20:06:10Z
dc.date.issued2017
dc.description.financeNie dotyczy
dc.description.volume50
dc.identifier.doi10.1088/1751-8121/AA8C69
dc.identifier.issn1751-8113
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/103537
dc.identifier.weblinkhttp://iopscience.iop.org/article/10.1088/1751-8121/aa8c69/meta
dc.languageeng
dc.pbn.affiliationphysical sciences
dc.relation.ispartofJournal of Physics A: Mathematical and Theoretical
dc.relation.pagesart. 435502
dc.rightsClosedAccess
dc.sciencecloudnosend
dc.titleConformal invariance of the Lungren–Monin–Novikov equations for vorticity fields in 2D turbulence
dc.typeJournalArticle
dspace.entity.typePublication