Error scaling of large-eddy simulation in the outer region of wall-bounded turbulence

We study the error scaling properties of large-eddy simulation (LES) in the outer region of wall-bounded turbulence at moderately high Reynolds numbers. In order to avoid the additional complexity of wall-modeling, we perform LES of turbulent channel flows in which the no-slip condition at the wall is replaced by a Neumann condition supplying the exact mean wall-stress. The statistics investigated are the mean velocity profile, turbulence intensities, and kinetic energy spectra. The errors follow (Δ/L)αReτγ, where Δ is the characteristic grid resolution, Reτ is the friction Reynolds number, and L is the meaningful length-scale to normalize Δ in order to collapse the errors across the wall-normal distance. We show that Δ can be expressed as the L2-norm of the grid vector and that L is well represented by the ratio of the friction velocity and mean shear. The exponent α is estimated from theoretical arguments for each statistical quantity of interest and shown to roughly match the values computed by numerical simulations. For the mean profile and kinetic energy spectra, α≈1, whereas the turbulence intensities converge at a slower rate α