Analytic prediction for planar turbulent boundary layers

Abstract

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 are the friction velocity $u_{\tau }$: $U_e/u_{\tau }\approx 2.22\ln R{e}_x+2.86-3.83\ln (\ln R{e}_x)$; the boundary layer thickness ${\delta }_e$: $x/{\delta }_e\approx 7.27\ln R{e}_x-5.18-12.52\ln (\ln R{e}_x)$; the momentum thickness Reynolds number: $R{e}_x/R{e}_{\theta }=4.94[(\ln {\mathrm{Re}}_{\theta }+1.88{)}^2+1]$, all in good agreement with empirical data.

5 pages, 2 figures