Boundary Layer Thickness and Friction Velocity by Symmetry Arguments

We derive analytically for the first time the downstream evolution of the boundary layer thickness and the friction velocity 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 and the leading-order similarity equations. An approximate leading-order solution was obtained using matched asymptotic expansions. The similarities and differences between ZPGTBL and turbulent channel flows in terms of the similarity equations are discussed to support the notion of leading-order universality of the near-wall layer.