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.
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Support from the DFG under project WA 3097/3-1 is gratefully acknowledged.
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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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DOI: https://doi.org/10.1007/978-3-319-29130-7_2
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