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 include the relations for momentum Reynolds number (Re θ) with friction Re τ and streamwise Re x : Re θ ≈ 3.27Re τ, and Re x /Re θ = 4.94 [(lnRe θ + 1.88)2 + 1]; the streamwise development of the friction velocity u τ: U e /u τ ≈ 2.22lnRe x + 2.86 − 3.83ln(lnRe x ), and of the boundary layer thickness δ e : x/δ e ≈ 7.27lnRe x −5.18−12.52ln(lnRe x ), which are fully validated by recent reliable data.
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