Infinite dimensional Lie algebra associated with conformal transformations of the two-point velocity correlation tensor from isotropic turbulence

Autor(es)

Grebenev, V. N. ^[1] ; Oberlack, M. ^[2] ; Grishkov, A. N. ^[3]

Afiliação do(s) autor(es)

^[1] Russian Acad Sci, Inst Computat Technol, Novosibirsk 630090 - Russia

^[2] Tech Univ Darmstadt, Dept Mech Engn, D-64287 Darmstadt - Germany

^[3] Univ Sao Paulo, Inst Math & Stat, BR-66281 Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK; v. 64, n. 3, p. 599-620, JUN 2013.
• Citações Web of Science: 2

Resumo

We deal with homogeneous isotropic turbulence and use the two-point velocity correlation tensor field (parametrized by the time variable t) of the velocity fluctuations to equip an affine space K (3) of the correlation vectors by a family of metrics. It was shown in Grebenev and Oberlack (J Nonlinear Math Phys 18:109-120, 2011) that a special form of this tensor field generates the so-called semi-reducible pseudo-Riemannian metrics ds (2)(t) in K (3). This construction presents the template for embedding the couple (K (3), ds (2)(t)) into the Euclidean space with the standard metric. This allows to introduce into the consideration the function of length between the fluid particles, and the accompanying important problem to address is to find out which transformations leave the statistic of length to be invariant that presents a basic interest of the paper. Also we classify the geometry of the particles configuration at least locally for a positive Gaussian curvature of this configuration and comment the case of a negative Gaussian curvature. (AU)

• Processo FAPESP: 11/50984-1 - Vladimir Grebenev | Russian Academy of Sciences - Siberian Division - Rússia
• Beneficiário: Alexandre Grichkov
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional