Analytic prediction for planar turbulent boundary layers

Analytic predictions of mean velocity profile（MVP） and streamwise（x） development of related integral quantities are presented for flows in channel and turbulent boundary layer（TBL）, based on a symmetry analysis of eddy length and total stress. Specific predictions include the relations for momentum Reynolds number（Reθ） with friction Reτ and streamwise Rex： Reθ≈ 3.27Reτ,and Rex/Reθ = 4.94（lnReθ ＋ 1.88）^2 ＋ 1; the streamwise development of the friction velocity uτ： Ue/uτ≈ 2.22 lnRex ＋ 2.86. 3.83ln（lnRex）, and of the boundary layer thickness δe： x/δe ≈ 7.27 lnRex.5.18.12.52ln（lnRex）, which are fully validated by recent reliable data.