Two-dimensional frequency-wave-number spectra [Fcy ](kx, ω) and [Fcy ](kz, ω) of the longitudinal velocity component are presented for the sublayer in fully developed turbulent pipe flow, at Reynolds numbers between 10600 and 46400. All of these sublayer spectra apparently scale by introducing dimensionless quantities based on a chara cteristic length scale ν/UT and a characteristic time scale ν/UT2.
Representative convection velocities have been obtained from the [Fcy ](kx ω) spectra. The characteristic convection velocity in the sublayer is independent of wave-number and is the same at all positions in the layer cx ≃ 8·0UT. This result has led to the conclusion that sublayer turbulence is wave-like.
Existing visualization data seem to indicate that the sublayer waves are also relatively periodic at least at low values of Reynolds number. Characteristic dimensions of the sublayer waves are λ+x ≃ 630, and λz+ = 135. Results of the visualization studies of Fage & Townend (1932) and of Runstadler, Kline & Reynolds (1963) and Kline et al. (1967) do not appear to conflict with a wave model for the sublayer.
All of the existing measurements of the sublayer have been for relatively low Reynolds numbers. Some of the present results for positions just outside the sublayer suggest that at Reynolds numbers greater than 30000, the structure and properties will change substantially from those observed to date. In particular the streaky structure which is commonly regarded as being characteristic of the sublayer will probably not be detected at sufficiently high Reynolds numbers.
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