Comparisons of theoretical profiles for a two-dimensional time-mean turbulent boundary layer with experimental data

Four theoretical models are considered for the time-mean velocity profile in a constant property turbulent boundary which is two-dimensional and steady in the time-mean sense. For the inner region of a turbulent boundary layer, the Van Driest (1956) and extended Van Driest models are compared with the more recent unsteady wall layer model. Comparisions with inner region data suggest that the unsteady wall layer model gives a better representation of the data; for this and theoretical reasons, it is suggested that the extended Van Driest model be abandoned. The unsteady wall layer model is then coupled with with two outer region models, namely the 'law of the wake' and an outer region similarity profile, to give two composite profiles for the entire boundary layer. Both profiles are compared with experimental data over a wide range of flow conditions. It is found that three parameter fits using the unsteady wall layer model and the 'law of the wake' give excellent representations of the data; however the data comparisons strongly suggest that the wall layer flow is not universal.