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‘Inactive’ motion and pressure fluctuations in turbulent boundary layers

Published online by Cambridge University Press:  28 March 2006

P. Bradshaw
Affiliation:
Aerodynamics Division, National Physical Laboratory, Teddington

Abstract

Townsend's (1961) hypothesis that the turbulent motion in the inner region of a boundary layer consists of (i) an ‘active’ part which produces the shear stress τ and whose statistical properties are universal functions of τ and y, and (ii) an ‘inactive’ and effectively irrotational part determined by the turbulence in the outer layer, is supported in the present paper by measurements of frequency spectra in a strongly retarded boundary layer, in which the ‘inactive’ motion is particularly intense. The only noticeable effect of the inactive motion is an increased dissipation of kinetic energy into heat in the viscous sublayer, supplied by turbulent energy diffusion from the outer layer towards the surface. The required diffusion is of the right order of magnitude to explain the non-universal values of the triple products measured near the surface, which can therefore be reconciled with universality of the ‘active’ motion.

Dimensional analysis shows that the contribution of the ‘active’ inner layer motion to the one-dimensional wave-number spectrum of the surface pressure fluctuations varies as τ2w/k1 up to a wave-number inversely proportional to the thickness of the viscous sublayer. This result is strongly supported by the recent measurements of Hodgson (1967), made with a much smaller ratio of microphone diameter to boundary-layer thickness than has been achieved previously. The disagreement of the result with most other measurements is attributed to inadequate transducer resolution in the other experiments.

Type
Research Article
Copyright
© 1967 Cambridge University Press

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References

Batchelor, G. K. 1953 The theory of homogeneous turbulence. Cambridge University Press.
Bradshaw, P. 1965 Nat. Phys. Lab. Aero Rept. no. 1172.
Bradshaw, P. 1967a Nat. Phys. Lab. Aero Rept. no. 1220.
Bradshaw, P. 1967b J. Fluid Mech. 27, 209.
Bradshaw, P. 1967c J. Fluid Mech. 29, 625.
Bradshaw, P. & Ferriss, D. H. 1966 Nat. Phys. Lab. Aero Rept. no. 1217.
Bradshaw, P., Ferriss, D. H. & Atwell, N. P. 1967 J. Fluid Mech. 28, 593.
Burton, R. A. 1965 Am. Inst. Aero Astro. J. 3, 784.
Chu, B. T. & Kovasznay, L. S. G. 1958 J. Fluid Mech. 3, 494.
Clark, J. A. 1966 Ph.D. Thesis, The Queens University, Belfast.
Corcos, G. M. 1963 J. Acoust. Soc. Am. 35, 192.
Corcos, G. M. 1964 J. Fluid Mech. 18, 353.
Foxwell, J. H. 1966 Admiralty Underwater Weapons Estab. Tech. Note 218/66.
Hodgson, T. H. 1967 Paper presented at Euromech. Colloquium, Southampton.
Karlsson, S. K. F. 1959 J. Fluid Mech. 5, 622.
Klebanoff, P. S. 1955 Nat. Adv. Comm. Aero (Wash.) Rept. no. 1247.
Phillips, O. M. 1955 Proc. Camb. Phil. Soc. 55, 220.
Reynolds, A. J. 1965 J. Fluid Mech. 22, 443.
Stratford, B. S. 1959 J. Fluid Mech. 5, 1.
Townsend, A. A. 1956 The structure of turbulent shear flow. Cambridge University Press.
Townsend, A. A. 1961 J. Fluid Mech. 11, 97.
Webb, E. K. 1964 Q. J. Roy. Met. Soc. 90, 344.
Willmarth, W. W. & Roos, F. W. 1965 J. Fluid Mech. 22, 81.
Willmarth, W. W. & Wooldridge, C. E. 1962 J. Fluid Mech. 14, 187.
Wills, J. A. B. 1965 Nat. Phys. Lab. Aero Rept. no. 1155.
Wills, J. A. B. 1967 Nat. Phys. Lab. Aero Rept. no. 1224.
Wooldridge, C. E. & Willmarth, W. W. 1962 Univ. of Michigan ORA Rept. no. 0-2920-2-T.