Large-eddy simulation of large-scale structures in long channel flow

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.