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

Citation:
Willis, GE, Deardorff JW, Somerville RCJ.  1972.  Roll-diameter dependence in Rayleigh convection and its effect upon the heat flux. Journal of Fluid Mechanics. 54:351-367.

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.

Notes:

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DOI:

10.1017/S0022112072000722