On the Difficulties in Resolving the Viscous Sublayer in Wall-Bounded Turbulence

Abstract

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 non-analytic 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.