Direct numerical simulation of heat transport in two-dimensional Rayleigh-Bénard convection

We investigate the heat transport efficiency in two-dimensional Rayleigh-Bénard convection with high resolution direct numerical simulation. The study is carried out in a box with unit aspect ratio in the Rayleigh number Ra range 10⁷ ~ 10¹² for Prandtl numbers Pr = 0.7 and 4.3. It is found that while the heat transport efficiency, i.e. Nusselt number Nu, scales as Ra^0.3 approximately over the whole Ra range, there exist obvious changes in the local scaling exponent of Nu-Ra relation in different Ra ranges, which could be understood with the changes in the flow structures and their dynamics.