On the difficulties in resolving the viscous sublayer in wall-bounded turbulence

Comparison of one-point statistics of turbulent velocities in the near-wall region y(+) < 10 from DNS of turbulent plane channel flows with corresponding data from experiments on wall-bounded turbulence show that DNS data are plagued by an overprediction of turbulent intensity and intermittency. This is the result of a spurious non-analyticity of logarithmic type, which arises from the violation by numerical approximations of a fine cancellation of high-order terms in y(+) in the equation for the wall-normal velocity component v. The arising nonanalytic additive error propagates into all hydrodynamic fields, but affects most strongly v which vanishes at the wall faster than the other velocity components. Its normalized moments like the flatness factor F-v are dominated by the error, with dramatic effects. For example, overprediction of F-v is larger in DNS with higher resolution. This paradoxical observation is explained by a simple model accounting for the high intermittency and for the log-errors of v near the wall.