The diagnostic plot - a new way to appraise turbulent boundary layer data

Most turbulent boundary layer data are obtained with hot-wire anemometry which gives access both to the mean ($U$) and turbulence intensity ($u^{\prime}$) distributions of the streamwise velocity. Comparisons between different measurements strongly depend on the accuracy of the determination of the friction velocity ($u_{\tau}$) and for comparisons in the near wall region the determination of the wall position is crucial. If $u^{\prime}$ is plotted as function of $U$, where both quantities are normalized by the free stream velocity ($U_{\infty}$) (hereafter called the {\it diagnostic plot}), any uncertainties in the wall position and $u_{\tau}$ are avoided when comparing different cases. For a given $Re$ all such distributions should fall on top of each other if $u^{\prime}$ and $U$ are accurately measured and the measurements are made in standard zero pressure gradient turbulent boundary layers. Close to the wall ($y^+<10$) the distribution is nearly self similar and independent of $Re$. Moreover the distribution should be linear with a constant slope ($\sim 0.40$) up to, at least, $y^+=3$ (corresponding to $U/U_{\infty} > 0.1$ for typical laboratory experiments) and thereafter the slope should decrease. The diagnostic plot clearly indicates at what position the measured values show a wall interference effect. Also in the outer region the distributions at different Reynolds numbers overlap, and the diagnostic plot has the interesting property that both the inner ($y^+<10$) and outer regions can be made to collapse in the same plot.