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New Statistical Symmetries of the Two-Point Correlation Equations for Turbulent Flows

  • Andreas M. RosteckEmail author
  • Martin Oberlack
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 141)

Abstract

We briefly introduce the two-point correlation equations based on the Navier-Stokes equations for an incompressible fluid. For this special case we determine the set of Lie symmetries, which can be calculated from the classical symmetries of the Navier-Stokes equations and further we present new symmetries, so called statistical symmetries. Finally we give examples where these symmetries can be used, e.g. for wall bounded turbulence and decaying turbulence scaling laws.

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References

  1. 1.
    George, W.K., Wang, H.: The exponential decay of homogeneous turbulence. Phys. Fluids 21, 025108 (2009)CrossRefGoogle Scholar
  2. 2.
    Hurst, D., Vassilicos, J.C.: Scalings and decay of fractal-generated turbulence. Phys. Fluids 19, 035103 (2007)CrossRefGoogle Scholar
  3. 3.
    Keller, L., Friedmann, A.: Differentialgleichungen für die turbulente Bewegung einer kompressiblen Flüssigkeit. In: Proc. First. Int. Congr. Appl. Mech., pp. 395–405 (1924)Google Scholar
  4. 4.
    Khujadze, G., Oberlack, M.: DNS and scaling laws from new symmetry groups of ZPG turbulent boundary layer flow. Theoret. Comput. Fluid Dyn. 18, 391–411 (2004)zbMATHCrossRefGoogle Scholar
  5. 5.
    Oberlack, M.: Symmetrie, Invarianz und Selbstähnlichkeit in der Turbulenz. Habilitation thesis. RWTH Aachen (2000)Google Scholar
  6. 6.
    Oberlack, M., Rosteck, A.: New statistical symmetries of the multi-point equations and its importance for turbulent scaling laws. Discrete Contin. Dyn. Syst., Ser. S 3, 451–471 (2010)MathSciNetGoogle Scholar
  7. 7.
    Seoud, R.E., Vassilicos, J.C.: Dissipation and decay of fractal-generated turbulence. Phys. Fluids 19, 105–108 (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Fluid Dynamics, Department of Mechanical EngineeringTU DarmstadtDarmstadtGermany
  2. 2.Center of Smart InterfacesTU DarmstadtDarmstadtGermany
  3. 3.GS Computational EngineeringTU DarmstadtDarmstadtGermany

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