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 ($Re_{\theta } )$ with friction $Re_{\tau } $ and streamwise $Re_{x} $:$Re_{\theta } \approx 3.27Re_{\tau } $ and$Re_{x} /Re_{\theta } =4.94[(\ln \mbox{Re}_{\theta } +1.88)^{2}+1]$; the streamwise development of the friction velocity$u_{\tau } $: $U_{e} /u_{\tau } \approx 2.22\ln Re_{x} +2.86-3.83\ln (\ln Re_{x} )$, and of the boundary layer thickness $\delta_{e} $:$x/\delta_{e} \approx 7.27\ln Re_{x} -5.18-12.52\ln (\ln Re_{x} )$, which are fully validated by recent reliable data.