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Roll-diameter dependence in Rayleigh convection and its effect upon the heat flux

Published online by Cambridge University Press:  29 March 2006

G. E. Willis ,
J. W. Deardorff  and
R. C. J. Somerville
G. E. Willis
Affiliation:
National Center for Atmospheric Research, Boulder, Colorado
J. W. Deardorff
Affiliation:
National Center for Atmospheric Research, Boulder, Colorado
R. C. J. Somerville
Affiliation:
Courant Institute of Mathematical Sciences, New York University Present address: Goddard Institute for Space Studies, N.A.S.A., 2880 Broadway, New York 10025.
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Abstract

The average roll diameter in Rayleigh convection for 2000 < R < 31000, where R is the Rayleigh number, has been measured from photographs of three convecting fluids: air, water and a silicone oil with a Prandtl number σ of 450. For air the average dimensionless roll diameter was found to depend uniquely upon R and to increase especially rapidly in the range 2000 < R < 8000. The fluids of larger σ exhibited strong hysteresis but also had average roll diameters tending to increase with R. The increase in average roll diameter with R tended to decrease with σ. Through use of two-dimensional numerical integrations for the case of air it was found that the increase in average roll diameter with R provides an explanation for the usual discrepancy in heat flux observed between experiment and two-dimensional numerical calculations which prescribe a fixed wavelength.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 54 , Issue 2 , 25 July 1972 , pp. 351 - 367
Copyright
© 1972 Cambridge University Press

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References

Busse, F. H. 1967 On the stability of two-dimensional convection in a layer heated from below J. Math. Phys. 46, 140–150.Google Scholar
Busse, F. H. & Whitehead, J. A. 1971 Instabilities of convection rolls in a high Prandtl number fluid J. Fluid Mech. 47, 305–320.Google Scholar
Davis, S. H. 1968 Convection in a box: on the dependence of preferred wavenumber upon the Rayleigh number at finite amplitude. J. Fluid Mech. 32, 619–624.Google Scholar
Deardorff, J. W. 1968 Examination of numerically calculated heat fluxes for evidence of a supercritical transition Phys. Fluids, 11, 1254–1256.Google Scholar
Deardorff, J. W. & Willis, G. E. 1965 The effect of two-dimensionality on the suppression of thermal turbulence J. Fluid Mech. 23, 337–353.Google Scholar
Foster, T. D. 1969 The effect of initial conditions and lateral boundaries on convection J. Fluid Mech. 37, 81–94.Google Scholar
Koschmieder, E. L. 1966 On convection on a uniformly heated plane Beit. Z. Phys. Atmos. 39, 1–11.Google Scholar
Krishnamurti, R. 1970 On the transition to turbulent convection. Part 1. The transition from two- to three-dimensional flow J. Fluid Mech. 42, 295–307.Google Scholar
Lipps, F. B. & Somerville, R. C. J. 1971 Dynamics of variable wavelength in finiteamplitude Bénard convection Phys. Fluids, 14, 759–765.Google Scholar
Malkus, W. V. R. 1954a Discrete transitions in turbulent convection. Proc. Roy. Soc A 225, 185–195.Google Scholar
Malkus, W. V. R. 1954b The heat transport and spectrum of thermal turbulence. Proc. Roy. Soc A 225, 196–212.Google Scholar
Nield, D. A. 1968 The Rayleigh—Jeffreys problem with boundary slab of finite conductivity J. Fluid Mech. 32, 393–398.Google Scholar
Rossby, H. T. 1969 A study of Bénard convection with and without rotation J. Fluid Mech. 36, 309–335.Google Scholar
Schlüter, A., Lortz, D. & Busse, F. H. 1965 On the stability of finite amplitude convection J. Fluid Mech. 23, 129–144.Google Scholar
Schmidt, R. J. & Saunders, O. A. 1938 On the motion of a fluid heated from below. Proc. Roy. Soc A 165, 216–228.Google Scholar
Somerscales, E. F. C. & Dougherty, T. S. 1970 Observed flow patterns at the initiation of convection in a horizontal liquid layer heated from below J. Fluid Mech. 42, 755–768.Google Scholar
Somerscales, E. F. C. & Dropkin, D. 1966 Experimental investigation of the temperature distribution in a horizontal layer of fluid heated from below Int. J. Heat Mass Transfer, 9, 1189–1204.Google Scholar
Somerville, R. C. J. 1970 Heat transfer in steady two-dimensional Bénard convection. Notes on the 1970 Summer Study Program in Geophysical Fluid Dynamics, Woods Hole Oceanographic Institution Rep. no. 70–50, I, 87–89.Google Scholar
Willis, G. E. & Deardorff, J. W. 1965 Measurements on the development of thermal turbulence in air between horizontal plates Phys. Fluids, 8, 2225–2229.Google Scholar
Willis, G. E. & Deardorff, J. W. 1967 Confirmation and renumbering of the discrete heat flux transitions of Malkus. Phys. Fluids, 10, 1861–1866.Google Scholar
Willis, G. E. & Deardorff, J. W. 1970 The oscillatory motions of Rayleigh convection J. Fluid Mech. 44, 661–672.Google Scholar