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Turbulence structure in thermal convection and shear-free boundary layers

Published online by Cambridge University Press:  20 April 2006

J. C. R. Hunt
J. C. R. Hunt
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW
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Abstract

This paper is a study of turbulence near rigid surfaces, in the absence of any mean shear. Different sources of turbulence are considered, including thermal convection and grid turbulence. It is shown that, if a rigid boundary is introduced into the flow, then for short times the linear theory of Hunt & Graham (1978) reveals the common structure of these flows near the boundary, if the parameters used are the rate of energy dissipation per unit mass ε and the distance z from the surface. Over longer times nonlinear effects develop, such as large eddies straining smaller eddies near the boundary. Some new estimates are suggested here and compared with the computations of Biringen & Reynolds (1981) and experiments of Thomas & Hancock (1977).

It is shown that calculations based on the linear theory agree well with many measurements of the vertical profiles of turbulence in thermal convection layers, including those of the vertical variance, the low-frequency end of the spectrum of the vertical turbulence (w), the integral scale of w, and two-point cross-correlations of w. (The latter was a prediction, subsequently tested by atmospheric measurements.) Some discussion of the reasons for this agreement are suggested. The observations of the effects of mean-velocity gradients near the surface are also shown to be consistent with the theoretical arguments proposed here.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 138 , January 1984 , pp. 161 - 184
Copyright
© 1984 Cambridge University Press

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References

Adrian, R. J. & Ferreira, R. T. S. 1979 In Turbulent Shear Flows 2 (ed. L. J. S. Bradbury et al.). Springer.
Arnal, D., Cousteix, J. & Michel, R. 1976 Recherche Aérospatiale no. 1. 13–16.
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Biringen, S. & Reynolds, W. C. 1981 J. Fluid Mech. 103, 53.
Bradshaw, P. 1978 J. Atmos. Sci. 35, 1768.
Carruthers, D. J. & Hunt, J. C. R. 1983 Velocity fluctuations near an interface between turbulence convection and a stable layer. (Submitted for publication.)
Caughey, S. J. & Palmer, S. G. 1979 Q. J. R. Met. Soc. 105, 811.
Deardorff, J. W. & Willis, G. E. 1974 Adv. Geophys. 18B, 197.
Durbin, P. A. 1979 Rapid distortion theory of turbulent flows. Ph.D. dissertation, University of Cambridge.
Durbin, P. A. 1981 Q. J. Mech. Appl. Maths 34, 489.
Graham, J. M. R. 1975 Imperial Coll. Aero. Tech. Note 75–101.
Hunt, J. C. R. 1983 In Proc. Symp. ‘Gas Transfer at Water Surfaces’, (ed. W. Brutsaert & G. H. Jirka). Reidel.
Hunt, J. C. R. & Graham, J. M. R. 1978 J. Fluid Mech. 84, 209.
Hunt, J. C. R., Kaimal, J. C. & Gaynor, J. 1984 Measurements of convective turbulence at Boulder Atmospheric Observatory. (Report in preparation.)
Kaimal, J. C. 1978 J. Atmos. Sci. 35, 18.
Kaimal, J. C., Wyngaard, J. C., Haugen, D. N., COTÉ, O. R., Izumi, Y., Caughey, S. J. & Readings, J. C. 1976 J. Atmos. Sci. 33, 2152.
Komori, S., Ueda, H., Ogino, F. & Mizushina, T. 1982 Intl J. Heat Mass Transfer 25, 513–521.
Lenschow, D. H. & Stephens, P. L. 1980 Boundary Layer Met. 19, 509.
Lenschow, D. H., Wyngaard, J. C. & Pennel, W. T. 1980 J. Atmos. Sci. 37, 1313.
Mcdougall, T. J. 1979 J. Fluid Mech. 94, 409.
Panofsky, H. A., Tennekes, H., Lenschow, D. H. & Wyngaard, J. C. 1977 Boundary Layer Meteor. 11, 335.
Priestley, C. H. B. 1959 Turbulent Transport in the Lower Atmosphere. University of Chicago Press.
Rodi, W. 1980 Turbulence Models and Their Applications in Hydraulics. I.A.H.R. Delft.
Thomas, N. H. & Hancock, P. E. 1977 J. Fluid Mech. 82, 481.
Townsend, A. A. 1976 Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.
Uzkan, T. & Reynolds, W. C. 1967 J. Fluid Mech. 28, 803.
Wilczak, J. M. & Tillman, J. E. 1980 J. Atmos. Sci. 37, 2424.
Wyngaard, J. C. 1979 In Turbulent Shear Flows 2 (ed. L. J. S. Bradbury et al.). Springer.
Wyngaard, J. C. & COTÉ, O. R. 1972 Q. J. R. Meteor. Soc. 98, 590.
Wyngaard, J. C., COTÉ, O. R. & Izumi, Y. 1971 J. Atmos. Sci. 28, 1171.