The energy budget in Rayleigh-Benard convection

It is shown using three series of Rayleigh number simulations of varying aspect ratio AR and Prandtl number Pr that the normalized dissipation at the wall, while significantly greater than 1, approaches a constant dependent upon AR and Pr. It is also found that the peak velocity, not the mean square velocity, obeys the experimental scaling of Ra^{0.5}. The scaling of the mean square velocity is closer to Ra^{0.46}, which is shown to be consistent with experimental measurements and the numerical results for the scaling of Nu and the temperature if there are strong correlations between the velocity and temperature.