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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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