Grebenev, Vladimir N. ; Oberlack, Martin ; Grishkov, A. N. (2013)
Infinite dimensional Lie algebra associated with conformal transformations of the two-point velocity correlation tensor from isotropic turbulence.
In: Zeitschrift für Angewandte Mathematik und Physik, 64 (3)
Artikel, Bibliographie
Kurzbeschreibung (Abstract)
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 R3 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.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2013 |
| Autor(en): | Grebenev, Vladimir N. ; Oberlack, Martin ; Grishkov, A. N. |
| Art des Eintrags: | Bibliographie |
| Titel: | Infinite dimensional Lie algebra associated with conformal transformations of the two-point velocity correlation tensor from isotropic turbulence |
| Sprache: | Englisch |
| Publikationsjahr: | Juni 2013 |
| Verlag: | Springer |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Zeitschrift für Angewandte Mathematik und Physik |
| Jahrgang/Volume einer Zeitschrift: | 64 |
| (Heft-)Nummer: | 3 |
| URL / URN: | http://link.springer.com/article/10.1007%2Fs00033-012-0251-7 |
| Kurzbeschreibung (Abstract): | 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 R3 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. |
| Fachbereich(e)/-gebiet(e): | 16 Fachbereich Maschinenbau 16 Fachbereich Maschinenbau > Fachgebiet für Strömungsdynamik (fdy) Exzellenzinitiative Exzellenzinitiative > Exzellenzcluster Zentrale Einrichtungen Exzellenzinitiative > Exzellenzcluster > Center of Smart Interfaces (CSI) |
| Hinterlegungsdatum: | 08 Okt 2014 08:41 |
| Letzte Änderung: | 20 Feb 2019 08:15 |
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