Reynolds Number Dependence of Streamwise Velocity Spectra in Turbulent Pipe Flow

Spectra of the streamwise velocity component in fully developed turbulent pipe flow are presented for Reynolds numbers up to [Formula presented]. 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, [Formula presented], is not expected, and any apparent [Formula presented] range does not attract any special significance and does not involve a universal constant. Reasons for this are suggested.