Comparison of turbulent thermal convection between conditions of constant temperature and constant flux

Rayleigh-Benard convection is the the buoyancy-driven flow of a fluid heated from below and cooled from above. It is of central importance for a variety of fundamental problems in the applied sciences and engineering, and it is one of the fundamental paradigms of complex nonlinear dynamics. However, the basic transport properties of turbulent convection are still not fully understood theoretically, and the experimental state of affairs is unsettled and even somewhat controversial. One proposal is that conflicting laboratory results are (in part) a consequence of different thermal boundary conditions employed in different experimental setups.

In this talk we report the results of high-resolution direct numerical simulations of the two-dimensional Boussinesq model of Rayleigh-Benard convection for Rayleigh numbers up to 10^10 in order to study the influence of temperature boundary conditions on turbulent heat transport. Specifically, we consider the extreme cases 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 for Rayleigh numbers above 10^7, and the overall flow dynamics for both scenarios, in particular, the time averaged temperature profiles, are also indistinguishable at the highest Rayleigh numbers. This is joint work with Hans Johnston, Department of Mathematics and Statistics, University of Massachusetts, that was recently published in Physical Review Letters Volume 102, 064501 (2009).