Prediction of boundary layer thickness and friction velocity of the zero-pressure-grasient trubulent boundary layer by symmetry arguments

We derive analytically for the first time the downstream evolution of the boundary layer thickness and the surface shear stress of the zero-pressure-gradient turbulent boundary layer (ZPGTBL). Lie groups were used to derive the downstream evolution and to obtain the full set of the similarity variables, the leading-order similarity equations, and an approximate leading-order solution. The similarities and differences between ZPGTBL and turbulent channel flows in terms of the similarity equations are discussed to support the notion of universality of the near-wall layer.