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Here we report the measurements of two-dimensional (2-D) spectra of thestreamwise velocity ($u$) in a high Reynolds number turbulent boundary layer. Anovel experiment employing multiple hot-wire probes was carried out at frictionReynolds numbers ranging from 2400 to 26000. Taylor's frozen turbulencehypothesis is used to convert temporal-spanwise information into a 2-D spatialspectrum 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 constantenergy level shows $\lambda_y/z \sim (\lambda_x/z)^{1/2}$ behaviour at largerscales, which is in agreement with the existing literature at a matchedReynolds number obtained from direct numerical simulations. However, at highReynolds numbers, it is observed that the square-root relationship tendstowards a linear relationship ($\lambda_y \sim \lambda_x$) as required forself-similarity and predicted by the attached eddy hypothesis.

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