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Progress in Turbulence VI pp 9–17Cite as

Complete Description of Turbulence in Terms of Hopf Functional and LMN Hierarchy: New Symmetries and Invariant Solutions

Part of the Springer Proceedings in Physics book series (SPPHY,volume 165)

Abstract

This paper deals with two methods for the full statistical description of turbulent field, namely the Lundgren–Monin–Novikov hierarchy (Lundgren, Phys Fluids, 10:969–975 1967, [5]) for the multipoint probability density functions (PDFs) of velocity and Hopf functional equation for turbulence (Hopf, J Ration Mech Anal, 1:87–122 1952, [2]). These equations are invariant under certain transformations of dependent and independent variables, so called symmetry transformation. The importance of these symmetries for the turbulence theory and modelling is discussed.

Keywords

  • Hopf Functional Equation
  • Full Descriptive Statistics
  • Ration Mech Anal
  • Probability Density Function
  • Galilei Invariance

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Acknowledgments

Support from the DFG under project WA 3097/3-1 is gratefully acknowledged.

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Authors and Affiliations

  1. Chair of Fluid Dynamics, Department of Mechanical Engineering, TU Darmstadt, Otto-Berndt Str. 2, 64287, Darmstadt, Germany

    Marta Wacławczyk

Authors
  1. Marta Wacławczyk
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Corresponding author

Correspondence to Marta Wacławczyk .

Editor information

Editors and Affiliations

  1. Inst of Phys, AG TWiSt, ForWind-CWER, Carl-von-Ossietzky University Oldenburg, Oldenburg, Germany

    Joachim Peinke

  2. Institute of Physics and ForWind, University of Oldenburg, Oldenburg, Niedersachsen, Germany

    Gerrit Kampers

  3. Department of Mechanical Engineering, TU Darmstadt, Darmstadt, Germany

    Martin Oberlack

  4. Department of Mechanical Engineering, TU Darmstadt, Darmstadt, Germany

    Marta Wacławczyk

  5. Dept of Indus Engg,Alma Mater Studiorum, Università di Bologna, Forlì, Italy

    Alessandro Talamelli

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Wacławczyk, M. (2016). Complete Description of Turbulence in Terms of Hopf Functional and LMN Hierarchy: New Symmetries and Invariant Solutions. In: Peinke, J., Kampers, G., Oberlack, M., Wacławczyk, M., Talamelli, A. (eds) Progress in Turbulence VI. Springer Proceedings in Physics, vol 165. Springer, Cham. https://doi.org/10.1007/978-3-319-29130-7_2

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