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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

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Acknowledgments

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

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Correspondence to Marta Wacławczyk .

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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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