Symmetry-induced high-moment turbulent velocity scaling laws of a spatially evolving turbulent round jet*

A direct numerical simulation (DNS) of a spatially evolving turbulent round jet is conducted at Re₀ = 3500 in a very large box using a fully turbulent pipe flow as an inlet to analyze classical and new scaling laws from the near up to the far-field. This simulation couples a DNS of a turbulent pipe flow with a DNS of a turbulent jet flow. Furthermore, symmetry analysis is performed on the multi-point moment equations (MPME) to derive turbulent scaling laws up to statistical moments of arbitrary order n for a spatially evolving turbulent round jet. The analysis unveils that the scaling law exponents of the higher moments are only dependent on the exponents of the first and second moments. The validation of the scaling laws with the DNS data reveal that the decay constants grow exponentially with n and that the scaling laws are fully described by five parameters. Further investigations show that the normalized instantaneous axial moments up to the tenth order are extremely well represented by a Gaussian function of the radius η = r/z. The prefactors of these exponents show a non-linear behavior in n. This suggests the existence of a statistical symmetry which, if confirmed, can only be found in the MPME rather than in the Navier-Stokes equations alone.