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

We report the results of high resolution direct numerical simulations of two-dimensional Rayleigh-B\'enard convection for Rayleigh numbers up to $Ra=10^{10}$ in order to study the influence of temperature boundary conditions on turbulent heat transport. Specifically, we considered the extremes of fixed heat flux (where the top and bottom boundaries are poor thermal conductors) and fixed temperature (perfectly conducting boundaries). Both cases display identical heat transport at high Rayleigh numbers fitting a power law $\nu \approx 0.138 \times Ra^{.285}$ with a scaling exponent indistinguishable from $2/7 = .2857$\dots above $Ra = 10^{7}$. The overall flow dynamics for both scenarios, in particular the time averaged temperature profiles, are also indistinguishable at the highest Rayleigh numbers.