Aspect-ratio dependence of heat transport by turbulent Rayleigh-Benard convection

We have studied the heat transport by steady circulating flows in two-dimensional rectangular cells of different values of the aspect ratio Gamma. The cells are heated from below and cooled on top with a fixed temperature difference. These steady circulating flows mimic the mean large-scale circulating wind observed in turbulent Rayleigh-Benard convection. When the heat transport is dominated by that carried by the mean large-scale wind and when the mean circulating wind is a single roll, we have found the following dependence of the Nusselt number (Nu) and the Reynolds number (Re) on the Rayleigh number (Ra), the Prandtl number (Pr) and the aspect ratio Gamma: Nu = B(Pr)N-0(Gamma) Ra-1/4 and Re = C(Pr)R-0(Gamma)Ra-1/2, where N-0(Gamma) decreases and R-0(Gamma) increases with Gamma.