Abstract
In this work we consider the statistical approach to turbulence represented by the Lundgren-Monin-Novikov (LMN) hierarchy of equations for the probability density functions (PDFs). After a review of the properties that the PDFs have to satisfy, we first show the basic Galilean invariance of the LMN equations; then we discuss the extended Galilean one and finally we present a transformation of the PDFs and examine the conditions which have to be satisfied so that this transformation represents a symmetry of the LMN hierarchy corresponding in the Multi-Point Correlation (MPC) approach to one of the so called statistical symmetries found using the Lie symmetry machinery in [6] for the infinite hierarchy of equations satisfied by the correlation functions from which some decay exponents of turbulent scaling law could be worked out.
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Staffolani, N., Waclawczyk, M., Oberlack, M., Friedrich, R., Wilczek, M. (2014). Lie Symmetries of the Lundgren−Monin−Novikov Hierarchy. In: Talamelli, A., Oberlack, M., Peinke, J. (eds) Progress in Turbulence V. Springer Proceedings in Physics, vol 149. Springer, Cham. https://doi.org/10.1007/978-3-319-01860-7_8
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DOI: https://doi.org/10.1007/978-3-319-01860-7_8
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-01859-1
Online ISBN: 978-3-319-01860-7
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