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Second-order invariants of the inviscid Lundgren–Monin–Novikov equations for 2d vorticity fields

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cris.lastimport.scopus2024-02-12T19:47:38Z
dc.abstract.enIn Grebenev, Wacławczyk, Oberlack (2019 Phys A: Math. Theor. 52, 33), the conformal invariance (CI) of the characteristic XX1(t) (the zero-vorticity Lagrangian path) of the first equation (i.e. for the evolution of the 1-point PDF f1(xx1,ω1,t), xx1∈D1⊂R2) of the inviscid Lundgren–Monin–Novikov (LMN) equations for 2d vorticity fields was derived. The infinitesimal operator admitted by the characteristics equation generates an infinite-dimensional Lie pseudo-group G which conformally acts on D1. We define the conformal invariant differential form ds2=f1⋅(dX112+dX212) along the characteristic XX1(t)|ω1=0 together with the simple action functional F(XX1,ds2). We demonstrate that GY, which is a subgroup of the group G restricted on the variables xx1 and f1, gives rise to a symmetry transformations of F(XX1,ds2). With this, we calculate the second-order universal differential invariant JY2 (or the multiscale representation of the invariants) of GY under the action on the zero-vorticity characteristics. We show that F(XX1,ds2) is a scalar invariant and generates all differential invariants, which look like the quantities of different scales, from JY2 by the operators of invariant differentiation. It gives insight into the geometry of a flow domain nearby point xx1 in the sense of Cartan.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorGrebenev, V. N.
dc.contributor.authorGrichkov, A. N.
dc.contributor.authorOberlack, M.
dc.contributor.authorWacławczyk, Marta
dc.date.accessioned2024-01-26T05:38:57Z
dc.date.available2024-01-26T05:38:57Z
dc.date.issued2021
dc.description.financePublikacja bezkosztowa
dc.description.number3
dc.description.volume72
dc.identifier.doi10.1007/S00033-021-01562-2
dc.identifier.issn0044-2275
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/119494
dc.identifier.weblinkhttps://link.springer.com/content/pdf/10.1007/s00033-021-01562-2.pdf
dc.languageeng
dc.pbn.affiliationphysical sciences
dc.relation.ispartofZeitschrift für Angewandte Mathematik und Physik
dc.relation.pages3-20
dc.rightsClosedAccess
dc.sciencecloudnosend
dc.subject.enLundgren–Monin–Novikov equations
dc.subject.enMultiscale representation of the invariants
dc.subject.enConformal symmetries
dc.subject.en2d vorticity field
dc.subject.enThe second-order universal differential invariant
dc.titleSecond-order invariants of the inviscid Lundgren–Monin–Novikov equations for 2d vorticity fields
dc.typeJournalArticle
dspace.entity.typePublication