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

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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.
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