Grebenev, Vladimir N. ; Oberlack, Martin (2009)
A Geometric Interpretation of the Second-Order Structure Function Arising in Turbulence.
In: Mathematical Physics, Analysis and Geometry, 12 (1)
Artikel, Bibliographie
Kurzbeschreibung (Abstract)
We primarily deal with homogeneous isotropic turbulence and use a closure model for the von Kármán-Howarth equation to study several geometric properties of turbulent fluid dynamics. We focus our attention on the application of Riemannian geometry methods in turbulence. Some advantage of this approach consists in exploring the specific form of a closure model for the von Kármán-Howarth equation that enables to equip a model manifold (a cylindrical domain in the correlation space) by a family of inner metrics (length scales of turbulent motion) which depends on time. We show that for large Reynolds numbers (in the limit of large Reynolds numbers) the radius of this manifold can be evaluated in terms of the second-order structure function and the correlation distance. This model manifold presents a shrinking cylindrical domain as time evolves. This result is derived by using a selfsimilar solution of the closure model for the von Kármán-Howarth equation under consideration. We demonstrate that in the new variables the selfsimilar solution obtained coincides with the element of Beltrami surface (or pseudo-sphere): a canonical surface of the constant sectional curvature equals − 1.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2009 |
| Autor(en): | Grebenev, Vladimir N. ; Oberlack, Martin |
| Art des Eintrags: | Bibliographie |
| Titel: | A Geometric Interpretation of the Second-Order Structure Function Arising in Turbulence |
| Sprache: | Englisch |
| Publikationsjahr: | 2009 |
| Verlag: | Springer |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Mathematical Physics, Analysis and Geometry |
| Jahrgang/Volume einer Zeitschrift: | 12 |
| (Heft-)Nummer: | 1 |
| URL / URN: | http://www.springerlink.com/content/c1k006pxg045x575/ |
| Kurzbeschreibung (Abstract): | We primarily deal with homogeneous isotropic turbulence and use a closure model for the von Kármán-Howarth equation to study several geometric properties of turbulent fluid dynamics. We focus our attention on the application of Riemannian geometry methods in turbulence. Some advantage of this approach consists in exploring the specific form of a closure model for the von Kármán-Howarth equation that enables to equip a model manifold (a cylindrical domain in the correlation space) by a family of inner metrics (length scales of turbulent motion) which depends on time. We show that for large Reynolds numbers (in the limit of large Reynolds numbers) the radius of this manifold can be evaluated in terms of the second-order structure function and the correlation distance. This model manifold presents a shrinking cylindrical domain as time evolves. This result is derived by using a selfsimilar solution of the closure model for the von Kármán-Howarth equation under consideration. We demonstrate that in the new variables the selfsimilar solution obtained coincides with the element of Beltrami surface (or pseudo-sphere): a canonical surface of the constant sectional curvature equals − 1. |
| Freie Schlagworte: | Beltrami surface; Closure model for the von Kármán-Howarth equation; Homogeneous isotropic turbulence; Riemannian metric; Two-point correlation tensor; Length scales of turbulent motion |
| Zusätzliche Informationen: | doi:10.1007/s11040-008-9049-4 |
| Fachbereich(e)/-gebiet(e): | 16 Fachbereich Maschinenbau > Fachgebiet für Strömungsdynamik (fdy) 16 Fachbereich Maschinenbau |
| Hinterlegungsdatum: | 24 Aug 2011 18:11 |
| Letzte Änderung: | 17 Feb 2014 08:46 |
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