A novel scaling framework for canonical smooth wall-bounded turbulent flows

Scaling of wall-bounded flows has been a long-standing issue. The scientific consensus leans towards piece-wise scaling, expressed in terms of velocity scaled using the friction velocity and the local Reynolds number. In this work, we propose a unified scaling function for the velocity based on the state-of-the-art understanding of propagation and interaction of scales in the wall-normal direction. We reconstruct the velocity profile by multiplying the scaling function by the depth of the flow and show that the recovered profile captures both the near-wall (inner) region and the outer region of the flow. We discuss the implications of such a scaling function on obtaining velocity profiles at infinite Reynolds numbers.