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

  • Marta WacławczykEmail author
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 165)


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.



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


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Chair of Fluid Dynamics, Department of Mechanical EngineeringTU DarmstadtDarmstadtGermany

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