Symmetry induced high-moment scaling laws of wall-bounded shear flows for arbitrary moments - validation using high Re_τ DNS and experimental data

Using symmetry-based turbulence theory, we derive turbulent scaling laws in wall-bounded shear flows for arbitrarily moments of U₁. Beside scaling of space and time, we use statistical symmetries, which are not directly observed in Navier-Stokes equations. These symmetries are admitted by the infinite hierarchy of moment and provide a measure of intermittency and non-Gaussianity. In the near-wall region the theory predicts a log-law for the mean velocity (n=1) and an algebraic law with the exponent ω (n - 1) for moments n > 1. Hence, the exponent w of the 2^nd moment determines the exponent of all higher moments. Moments here always refer to the instantaneous velocities U and not to the fluctuations u’. For the core regions of both plane and round Poiseuille flows we find an algebraic deficit law for arbitrary moments n with a scaling exponent n(σ₂-σ₁)+2σ₁-σ₂. Hence, the moments of order one and two with its scaling exponents σ₁ and σ₂  determine all higher exponents. All new results are validated by a new plane Poiseuille flow DNS at Re_τ=10⁴ and by pipe flow data from the CICLoPE and Superpipe flow experiments up to Re_τ=3.8*10⁴. We find that σ₁ and σ₂ are almost identical, so that the exponents of all moments are essentially constant, which corresponds to anomalous scaling.