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On the wave structure of the wall region of a turbulent boundary layer

Published online by Cambridge University Press:  29 March 2006

Fritz H. Bark
Fritz H. Bark
Affiliation:
Department of Mechanics, Royal Institute of Technology, Stockholm
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Abstract

Following the ideas suggested by Landahl (1967, 1975), some model calculations of the fluctuating velocity field in the wall region of a turbulent boundary layer have been carried out. It was assumed that the turbulent stresses are generated intermittently on small scales in time and space owing to bursting-type motions. The Reynolds-stress distribution during bursting periods and the mean velocity profile were assumed to be known, and the linear large-scale response to a random system of bursts was computed using an idealized model for the joint probability distribution in time and space of the occurrence of bursts. Computed energy spectra of the streamwise velocity fluctuations display scales in the spanwise and streamwise directions and time which are in good agreement with measurements by Morrison, Bullock & Kronauer (1971). However, the wavenumber band-widths of the computed spectra are narrower than those of the measured ones. This discrepancy is probably due to the crudeness of the model employed for the Reynolds stress during bursting.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 70 , Issue 2 , 29 July 1975 , pp. 229 - 250
Copyright
© 1975 Cambridge University Press

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References

Bakewell, H. P. & Lumley, J. L. 1967 Phys. Fluids, 10, 1880.
Bark, F. H. 1974 Ph.D. thesis, Dept. Mech., Roy. Inst. Tech., Stockholm.
Blackwelder, R. F. & Kaplan, R. E. 1972 AGARD Conf. Proc. p. 93.
Brodkey, R. S., Wallace, J. M. & Eckelmann, H. 1974 J. Fluid Mech. 63, 209.
Büssman, K. & MÜNZ, H. 1942 Jb. Dtsch. Luftfahrtf. 1, 36.
Coles, D. 1956 J. Fluid Mech. 1, 191.
Corino, E. R. & Brodkey, R. S. 1969 J. Fluid Mech. 37, 1.
Eckhaus, W. 1965 Studies in Non-Linear Stability Theory. Springer.
Gupta, A. K., Laufer, J. & Kaplan, R. E. 1971 J. Fluid Mech. 50, 493.
Hinze, J. O. 1957 Turbulence. McGraw-Hill.
Kim, H. T., Kline, S. J. & Reynolds, W. C. 1971 J. Fluid Mech. 50, 133.
Klebanoff, P. S. 1954 N.A.C.A. Tech. Note, no. 3178.
Klebanoff, P. S., Tidstrom, K. D. & Sargent, L. M. 1962 J. Fluid Mech. 12, 1.
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 J. Fluid Mech. 30, 741.
Kovasznay, L. S. G. 1973 Symposia Matematica del Istituto Nazionale di Alta Matematica, vol. 9, p. 507. Academic.
Lahey, R. T. & Kline, S. J. 1971 Thermosci. Div., Dept. Mech. Engng, Stanford University, Rep. MD-26.
Landahl, M. T. 1967 J. Fluid Mech. 29, 44.
Landahl, M. T. 1972 J. Fluid Mech. 56, 775.
Landahl, M. T. 1975 SIAM J. Appl. Math. (to appear).
Laufer, J. & Badri narayanan, M. A. 1971 Phys. Fluids, 14, 182.
Lighthill, M. J. 1952 Proc. Roy. Soc. A 211, 564.
Lumley, J. L. 1965 Proc. Int. Coloq. on Fine-Scale Processes in the Atmosphere and Their Influence on Radio-Wave Propagation. Moscow: Dokl. Akad. Nauk.
Morrison, W. R. B., Bullock, K. J. & Kronauer, R. E. 1971 J. Fluid Mech. 47, 639.
Morrison, W. R. B. & Kronauer, R. E. 1969 J. Fluid Mech. 39, 117.
Offen, G. R. & Kline, S. J. 1974 J. Fluid Mech. 62, 223.
Rao, K. N., Narasimha, R. & Badri narayanan, M. A. 1971 J. Fluid Mech. 48, 339.
Rice, S. O. 1944 Bell System Tech. J. no. 23–24.
Schubert, G. & Corcos, G. M. 1967 J. Fluid Mech. 29, 113.
Squire, H. B. 1993 Proc. Roy. Soc. A 142, 621.
Sternberg, J. 1965 AGARDograph, no. 97, part 1, p. 1.
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow. Cambridge University Press.
Wallace, J. M., Eckelmann, H. & Brodkey, R. S. 1972 J. Fluid Mech. 54, 39.
Willmarth, W. W. & Lu, S. S. 1972 J. Fluid Mech. 55, 65.
Willmarth, W. W. & Lu, S. S. 1973 J. Fluid Mech. 60, 481.
Willmarth, W. W. & Wooldridge, C. E. 1962 J. Fluid Mech. 14, 187.