Local equilibrium approximation in free turbulent flows: Verification through the method of differential constrains

Autor(es)

Grebenev, Vladimir N. ^[1] ; Demenkov, Andrew G. ^{[2, 3]} ; Chernykh, Gennady G. ^[1] ; Grichkov, Alexandre N. ^{[4, 5]}

Afiliação do(s) autor(es)

^[1] Fed Res Ctr Informat & Computat Technol, Lavrentjev Ave 6, Novosibirsk 630090 - Russia

^[2] Russian Acad Sci, Kutateladze Inst Thermophys, Siberian Branch, Lavrentjev Ave 1, Novosibirsk 630090 - Russia

^[3] Novosibirsk State Tech Univ, Pr K Marksa 20, Novosibirsk 630073 - Russia

^[4] Univ Sao Paulo, Inst Math & Stat, Rua Matao 1010, BR-66281 Sao Paulo - Brazil

^[5] Omsk AMFM Dostoevsky State Univ, Litskevich 1, Omsk 644053 - Russia

• Tipo de documento: Artigo Científico
• Fonte: ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK; v. 101, n. 9 SEP 2021.
• Citações Web of Science: 0

Resumo

We present a full version of the results obtained in Grebenev et al {[}Doklady Physics 47(7), 518-521 (2002)] wherein the closure formula, that is, the local equilibrium approximation of second-order moments for modeling free turbulent flows was justified by the method of differential constrains. The proposed analysis provides us a point of view from the modern theory of symmetry analysis on the closure problem in turbulence. Specifically, closure relationships in the physical space are interpreted as the (differential) equations of invariant sets (manifolds) in a phase-space. We demonstrate how this concept can be applied for verification of the local equilibrium approximations (LEA) of second-order moments. With this, we obtain the equivalence of LEA and vanishing the Poisson bracket for the defect of the longitudinal velocity component and of the turbulent energy. Numerical experiments carried out in a far turbulent wake confirm this conclusion. (AU)

• Processo FAPESP: 18/21330-2 - Conjunto mínimo de invariantes diferenciais do grupo de laços que aparece na teoria de fluidos
• Beneficiário: Alexandre Grichkov
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional