  Near-wall turbulent velocities in turbulent channel flows are decomposed into
small-scale and large-scale components at $y^+<100$ by improving the predictive
inner-outer model of Baars et al. [Phys. Rev. Fluids 1, 054406 (2016)], where
$y^+$ is the viscous-normalized wall-normal height. The small-scale one is
obtained by reducing the outer reference height (a parameter in the model) from
the center of the logarithmic layer to $y^+=100$, which can fully remove outer
influences. On the other hand, the large-scale one represents the near-wall
footprints of outer energy-containing motions. We present plenty of evidences
that demonstrate that the small-scale motions are Reynolds-number invariant
with the viscous scaling, at friction Reynolds numbers between 1000 and 5200.
At lower Reynolds numbers from 180 to 600, the small scales can not be scaled
by the viscous units, and the vortical structures are progressively
strengthened as Reynolds number increases, which is proposed as a possible
mechanism responsible for the anomalous scaling behavior. Finally, it is found
that a small-scale part of the outer large-scale footprint can be well scaled
by the viscous units.
