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