  The QSQH theory is extended to all three velocity components taking into
account the fluctuations of the direction of the large-scale component of the
wall friction. This effect is found to be significant. It explains the large
sensitivity of the fluctuations of longitudinal and spanwise velocities to
variations in the Reynolds number in comparison with the sensitivity of the
mean velocity, the Reynolds stress, and the wall-normal velocity fluctuations.
The analysis shows that the variation of the longitudinal velocity fluctuations
with the Reynolds number is dominated by the variation of the amplitude and
wall-normal-scale modulation of the universal mean velocity profile by the
outer, large-scale, Reynolds-number-dependent motions. The variation of
spanwise velocity fluctuations is dominated by the fluctuations of the
direction of the large-scale component of the wall friction. The Reynolds
number dependence of the other second moments is not dominated by these
mechanisms because the mean wall-normal velocity and the mean spanwise velocity
are zero. Explicit relationships between the differences in the second moments
of velocity in any two high-Reynolds-number near-wall flows were derived. The
comparisons gave a satisfactory agreement for the root-mean square of the
wall-parallel velocity components in the range of the distances from the wall
where modulation by large-scale motions dominates. Relationships between the
differences of the constants of the logarithmic law, the shape of the mean
velocity profile, and the differences of the second moments of velocity caused
by the differences in large-scale motions were derived and estimated
quantitatively.
