A scaling improved inner-outer decomposition of near-wall turbulent motions

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.