Wall turbulence at $Re_\tau=10k$: Kinematics and Symmetry scaling laws*

A new direct numerical simulation of a Poiseuille channel flow has been conducted for a friction Reynolds number of 10 000, extending a recent work published in PRL/PRF. Therein, we have shown using symmetry theory that the logarithmic law of the mean streamwise velocity and a related power-law for arbitrarily high moments is a valid solution to the multi-point moment equations. The DNS confirmed a long region of validity extending from 400 to 2500 wall units. Similarly, symmetry theory also gave rise to a related power-law scaling of arbitrary moments of the streamwise velocity in the center/deficit region of the channel. The DNS data also confirmed it. The symmetry theory has now been extended to scaling the moments of the wall-normal and spanwise velocities both in the near-wall and center region. Our most recent DNS data confirm this. About the flow's kinematics, the maximum intensity of the streamwise velocity increases with the Reynolds number, as was thought. The collapse of the turbulent budgets is perfect above 25 wall units. About the well-known scaling failure of the dissipation, we have computed the value of the near-wall gradient of u' for several Reynolds numbers. Our data confirm this value's relationship to the

dissipation scaling failure.