Streamwise velocity statistics in turbulent boundary layers that spatially develop to high Reynolds number

Well-resolved measurements of the streamwise velocity in zero pressure gradient turbulent boundary layers are presented for friction Reynolds numbers up to 19,670. Distinct from most studies, the present boundary layers undergo nearly a decade increase in Reynolds number solely owing to streamwise development. The profiles of the mean and variance of the streamwise velocity exhibit logarithmic behavior in accord with other recently reported findings at high Reynolds number. The inner and mid-layer peaks of the variance profile are evidenced to increase at different rates with increasing Reynolds number. A number of statistical features are shown to correlate with the position where the viscous force in the mean momentum equation loses leading order importance, or similarly, where the mean effect of turbulent inertia changes sign from positive to negative. The near-wall peak region in the 2-D spectrogram of the fluctuations is captured down to wall-normal positions near the edge of the viscous sublayer at all Reynolds numbers. The spatial extent of this near-wall peak region is approximately invariant under inner normalization, while its large wavelength portion is seen to increase in scale in accord with the position of the mid-layer peak, which resides at a streamwise wavelength that scales with the boundary layer thickness.