Examination of Numerically Calculated Heat Fluxes for Evidence of a Supercritical Transition

Numerical integrations of two‐dimensional convection between rigid horizontal boundaries performed by the author and others for small Rayleigh numbers, for a Prandtl number of unity, and for a fundamental wavelength of twice the height, are examined closely to see if they reproduce the experimental result that $\mathrm{NR\hspace{0.17em}=\hspace{0.17em}aR\; -\; b}$ , where N is the Nusselt number and R the Rayleigh number. If only one mode of convection were present, this linear law would be obeyed. The presence of higher modes in the calculations causes NR to gradually increase faster than the linear law as R increases. It is concluded that the discrete transitions of Malkus are not associated with instability of higher vertical modes when the convection is forced to be two dimensional with a fixed maximum horizontal wavelength.