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.