Oberlack, Martin ; Khujadze, George
Hrsg.: Peinke, Joachim ; Oberlack, Martin ; Talamelli, Alessandro (2009)
Fractal-Generated Turbulent Scaling Laws from a New Scaling Group of the Multi-Point Correlation Equation.
In: Progress in Turbulence III: Proceedings of the iTi Conference in Turbulence 2008
Buchkapitel, Bibliographie
Kurzbeschreibung (Abstract)
Investigating the multi-point correlation (MPC) equations for the velocity and pressure fluctuations in the limit of homogeneous turbulence a new scaling symmetry has been discovered. Interesting enought this property is not shared with the Euler or Navier-Stokes equations from which the MPC equations have orginally emerged. This was first observed for parallel wall-bounded shear flows (see [2]) though there this property only holds true for the two-point equation. Hence, in a strict sense there it is broken for higher order correlation equations. Presently using this extended set of symmetry groups a much wider class of invariant solutions or turbulent scaling laws is derived for homogeneous and homogeneous-isotropic turbulence which is in stark contrast to the classical power law decay arising from Birkhoff’s or Loitsiansky’s integrals. In particular, we show that the experimentally observed specific scaling properties of fractal-generated turbulence (see [1, 4]) fall into this new class of solutions. Due to this specific grid a breaking of the classical scaling symmetries due to a wide range of scales acting on the flow is accomplished. This in particular leads to a constant integral and Taylor length scale downstream of the fractal grid and the exponential decay of the turbulent kinetic energy along the same axis. These particular properties can only be conceived from MPC equations using the new scaling symmetry. The latter new scaling law may have been the first clear indication towards the existence of the extended statistical scaling group. Though the latter is not obvious from the instantaneous Euler or Navier-Stokes equations it is directly implied.
| Typ des Eintrags: | Buchkapitel |
|---|---|
| Erschienen: | 2009 |
| Herausgeber: | Peinke, Joachim ; Oberlack, Martin ; Talamelli, Alessandro |
| Autor(en): | Oberlack, Martin ; Khujadze, George |
| Art des Eintrags: | Bibliographie |
| Titel: | Fractal-Generated Turbulent Scaling Laws from a New Scaling Group of the Multi-Point Correlation Equation |
| Sprache: | Englisch |
| Publikationsjahr: | 2009 |
| Ort: | http://dx.doi.org/10.1007/978-3-642-02225-8_3 |
| Verlag: | Springer |
| (Heft-)Nummer: | 131 |
| Buchtitel: | Progress in Turbulence III: Proceedings of the iTi Conference in Turbulence 2008 |
| Reihe: | Springer Proceedings in Physics |
| Kurzbeschreibung (Abstract): | Investigating the multi-point correlation (MPC) equations for the velocity and pressure fluctuations in the limit of homogeneous turbulence a new scaling symmetry has been discovered. Interesting enought this property is not shared with the Euler or Navier-Stokes equations from which the MPC equations have orginally emerged. This was first observed for parallel wall-bounded shear flows (see [2]) though there this property only holds true for the two-point equation. Hence, in a strict sense there it is broken for higher order correlation equations. Presently using this extended set of symmetry groups a much wider class of invariant solutions or turbulent scaling laws is derived for homogeneous and homogeneous-isotropic turbulence which is in stark contrast to the classical power law decay arising from Birkhoff’s or Loitsiansky’s integrals. In particular, we show that the experimentally observed specific scaling properties of fractal-generated turbulence (see [1, 4]) fall into this new class of solutions. Due to this specific grid a breaking of the classical scaling symmetries due to a wide range of scales acting on the flow is accomplished. This in particular leads to a constant integral and Taylor length scale downstream of the fractal grid and the exponential decay of the turbulent kinetic energy along the same axis. These particular properties can only be conceived from MPC equations using the new scaling symmetry. The latter new scaling law may have been the first clear indication towards the existence of the extended statistical scaling group. Though the latter is not obvious from the instantaneous Euler or Navier-Stokes equations it is directly implied. |
| Zusätzliche Informationen: | DOI: 10.1007/978-3-642-02225-8_3 |
| Fachbereich(e)/-gebiet(e): | 16 Fachbereich Maschinenbau > Fachgebiet für Strömungsdynamik (fdy) 16 Fachbereich Maschinenbau |
| Hinterlegungsdatum: | 02 Sep 2011 13:15 |
| Letzte Änderung: | 17 Feb 2014 08:46 |
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