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

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 26 000. 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 similar to(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) similar to lambda(x)), as required for self-similarity and predicted by the attached eddy hypothesis.