  We investigate statistics of large-scale structures from large-eddy
simulation (LES) of turbulent channel flow at friction Reynolds numbers
$Re_\tau = 2 {\rm k}$ and $200 {\rm k}$. To properly capture the behaviour of
large-scale structures, the channel length is chosen to be 96 times the channel
half-height. In agreement with experiments, these large-scale structures are
found to give rise to an apparent amplitude modulation of the underlying
small-scale fluctuations. This effect is explained in terms of the phase
relationship between the large- and small-scale activity. The shape of the
dominant large-scale structure is investigated by conditional averages based on
the large-scale velocity, determined using a filter width equal to the channel
half-height. The conditioned field demonstrates coherence on a scale of several
times the filter width, and the small-scale--large-scale relative phase
difference increases away from the wall, passing through $\pi/2$ in the overlap
region of the mean velocity before approaching $\pi$ further from the wall. We
also found that, near the wall, the convection velocity of the large-scales
departs slightly, but unequivocally, from the mean velocity.
