Spectra of the streamwise velocity component in fully developed turbulent pipe flow are presented for Reynolds numbers up to $5.7\times {10}^6$. Even at the highest Reynolds number, streamwise velocity spectra exhibit incomplete similarity only: while spectra collapse with both classical inner and outer scaling for limited ranges of wave number, these ranges do not overlap. Thus similarity may not be described as complete, and a region varying with the inverse of the streamwise wave number, $k_1$, is not expected, and any apparent $k_1^{-1\mathrm{}}$ range does not attract any special significance and does not involve a universal constant. Reasons for this are suggested.

• Received 11 September 2001

DOI:https://doi.org/10.1103/PhysRevLett.88.214501