Lie Symmetries of the Lundgren−Monin−Novikov Hierarchy
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  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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