Two-dimensional energy spectra in high Reynolds number turbulent boundary layers

Abstract

Here we report the measurements of two-dimensional (2-D) spectra of the streamwise velocity ($u$) in a high Reynolds number turbulent boundary layer. A novel experiment employing multiple hot-wire probes was carried out at friction Reynolds numbers ranging from 2400 to 26000. Taylor's frozen turbulence hypothesis is used to convert temporal-spanwise information into a 2-D spatial spectrum which shows the contribution of streamwise (${\lambda }_x$) and spanwise (${\lambda }_y$) length scales to the streamwise variance at a given wall height ($z$). At low Reynolds numbers, the shape of the 2-D spectra at a constant energy level shows ${\lambda }_y/z\sim ({\lambda }_x/z{)}^{1/2}$ behaviour at larger scales, which is in agreement with the existing literature at a matched Reynolds number obtained from direct numerical simulations. However, at high Reynolds numbers, it is observed that the square-root relationship tends towards a linear relationship (${\lambda }_y\sim {\lambda }_x$) as required for self-similarity and predicted by the attached eddy hypothesis.

11 pages, 6 figures