Wall turbulence at high friction Reynolds numbers

A new direct numerical simulation of a Poiseuille channel flow has been conducted for a friction Reynolds number of 10000, using the pseudospectral code LISO. The mean streamwise velocity presents a long logarithmic layer, extending from 400 to 2500 wall units, longer than it was thought. The maximum of the intensity of the streamwise velocity increases with the Reynolds number, as expected. Also, the elusive second maximum of this intensity has not appeared yet. In case it exists, its location will be around y(+) approximate to 120, for a friction Reynolds number extrapolated to approximately 13 500. The small differences in the near-wall gradient of this intensity for several Reynolds numbers are related to the scaling failure of the dissipation, confirming this hypothesis. The scaling of the turbulent budgets in the center of the channel is almost perfect above 1000 wall units. Finally, the peak of the pressure intensity grows with the Reynolds number and does not scale in wall units. If the pressure at the wall is modeled as an inverse quadratic power of Re-tau, then p(infinity)'(+) approximate to 4.7 at the limit of infinite Reynolds number.