  A theoretical description of the phenomenon of modulation of near-wall
turbulence by large scale structures is investigated. The description given is
simple in that the effect of large-scale structures is limited to a
quasi-steady response of the near-wall turbulence to slow large-scale
fluctuations of the skin friction. The most natural and compact form of
expressing this mechanism is given by the usual Reynolds-number-independent
representation of the total skin friction and velocity, scaled in wall
variables, where the mean quantities are replaced by large-scale
low-pass-filtered fluctuating components. The theory is rewritten in terms of
fuctuations via a universal mean velocity and random mean square fluctuation
velocity profiles of the small-scales and then linearised assuming that the
large-scale fluctuations are small as compared to the mean components. This
allows us to express the superposition and modulation coefficients of the
empirical predictive models of the skin friction and streamwise fluctuating
velocity given respectively by Marusic et al. (13th Eur. Turb. Conf., 2011) and
Mathis et al. (J. Fluid Mech. 2011, vol. 681, pp. 537-566). It is found that
the theoretical quantities agree well with experimentally determined
coefficients.
