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We report the results of high resolution direct numerical simulations oftwo-dimensional Rayleigh-B\'enard convection for Rayleigh numbers up to$\Ra=10^{10}$ in order to study the influence of temperature boundaryconditions on turbulent heat transport. Specifically, we considered the extremecases of fixed heat flux (where the top and bottom boundaries are poor thermalconductors) and fixed temperature (perfectly conducting boundaries). Both casesdisplay identical heat transport at high Rayleigh numbers fitting a power law$\Nu \approx 0.138 \times \Ra^{.285}$ with a scaling exponent indistinguishablefrom $2/7 = .2857...$ above $\Ra = 10^{7}$. The overall flow dynamics for bothscenarios, in particular the time averaged temperature profiles, are alsoindistinguishable at the highest Rayleigh numbers. The findings are comparedand contrasted with results of recent three-dimensional simulations.

A Comparison of Turbulent Thermal Convection Between Conditions of Constant Temperature and Constant Flux