  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 $(\Delta/L)^{\alpha}Re_\tau^{\gamma}$, where
$\Delta$ is the characteristic grid resolution, $Re_\tau$ is the friction
Reynolds number, and $L$ is the meaningful length-scale to normalize $\Delta$
in order to collapse the errors across the wall-normal distance. We show that
$\Delta$ can be expressed as the $L_2$-norm of the grid vector and that $L$ is
well represented by the ratio of the friction velocity and mean shear. The
exponent $\alpha$ 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,
$\alpha\approx1$, whereas the turbulence intensities converge at a slower rate
$\alpha<1$. The exponent $\gamma$ is approximately $0$, i.e. the LES solution
is independent of the Reynolds number. The expected behavior of the turbulence
intensities at high Reynolds numbers is also derived and shown to agree with
the classic log-layer profiles for grid resolutions lying within the inertial
range. Further examination of the LES turbulence intensities and spectra
reveals that both quantities resemble their filtered counterparts from direct
numerical simulation (DNS) data, but that the mechanism responsible for this
similarity is related to the balance between the input power and dissipation
rather than to filtering.
