Origin of the scaling laws of developing turbulent boundary layers

In this Perspective article, we seek the origin of scaling laws developing turbulent boundary layers over a flat plate from perspective phenomenological theory turbulence. The boundary-layer thickness and shear stress in rough smooth flows are established. flow, (scaled with roughness) dynamic pressure) obey “2/(1− σ)” “(1+ σ)/(1− laws, respectively, streamwise distance roughness). Here, σ is spectral exponent. viscous length scale) “8/(5 − 3 “3(1+ σ)/(5 Reynolds number characterized by distance.