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Experimental evidence of waves in the sublayer

Published online by Cambridge University Press:  29 March 2006

W. R. B. Morrison ,
K. J. Bullock  and
R. E. Kronauer
W. R. B. Morrison
Affiliation:
Department of Mechanical Engineering, University of Queensland, Australia Present address: Oceanics Australia, Brisbane, Australia
K. J. Bullock
Affiliation:
Department of Mechanical Engineering, University of Queensland, Australia
R. E. Kronauer
Affiliation:
Harvard University, Cambridge, Mass., U.S.A.
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Abstract

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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 47 , Issue 4 , 29 June 1971 , pp. 639 - 656
Copyright
© 1971 Cambridge University Press

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References

Bakewell, H. P. & Lttmley, J. L. 1967 Viscous sublayer and adjacent wall region in turbulent pipe flow Phys. Fluids, 10, 1880.Google Scholar
Einstein, H. A. & Li, H. 1956 The viscous sublayer along a smooth boundary Am. Soc. Civil Engrs Proc. 82, 945.Google Scholar
Fage, A. & Townend, H. C. H. 1932 An examination of turbulent flow with an ultramicroscope. Proc. Roy. Soc. A 135, 656.Google Scholar
Hanratty, T. J. 1956 Turbulent exchange of mass and momentum with a boundary J. Am. Inst. Chem. Engrs, 2, 359.Google Scholar
Kline, S. J. 1967 Observed structure features in turbulent and transitional boundary layers. Gen. Motors Symposium on Internal Flow. Amsterdam: Elsevier.
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers J. Fluid Mech. 30, 741.Google Scholar
Kline, S. J. & Runstadler, P. W. 1959 Some preliminary results of visual studies of wall layers of the turbulent boundary layer. ASME Trans. J. Appl. Mech. 166.Google Scholar
Laufer, J. 1954 The structure of turbulence in fully developed pipe flow. NACA Rep. 1174.Google Scholar
Morrison, W. R. B. 1969 Two-dimensional frequency-wavenumber spectra and narrow band shear stress correlations in turbulent pipe flow. Ph.D. thesis, Department of Mechanical Engineering, University of Queensland.
Morrison, W. R. B. & Kronauer, R. E. 1969 Structural similarity for fully developed turbulence in smooth tubes J. Fluid Mech. 39, 117.Google Scholar
Runstadler, P. W., Kline, S. J. & Reynolds, W. C. 1963 An experimental investigation of the flow structure of the turbulent boundary layer. Rep. MD-8, Thermosciences Div., Mech. Engr. Dep., Stanford University.
Schraub, F. A., Kline, S. J., Henry, J., Runstadler, P. W. & Little, A. 1965 Use of hydrogen bubbles for quantitative determination of time dependent velocity fields in low speed water flows. ASME Trans. J. Basic Eng. 429.Google Scholar
Schubert, G. & Corcos, G. M. 1967 The dynamics of turbulence near a wall according to a linear model J. Fluid Mech. 29, 113.Google Scholar
Sternberg, J. 1962 A theory for the viscous sublayer of a turbulent flow J. Fluid Mech. 13, 241.Google Scholar
Sternberg, J. 1965 AGARDOGRAPH 97 (1st Paper).
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow. Cambridge University Press.
Wills, J. A. B. 1964 On convection velocities in turbulent shear flows J. Fluid Mech. 20, 417.Google Scholar