Convective turbulence in a Rayleigh-Benard system with and without rotation in the infinite Prandtl number limit

Convective turbulence in a Rayleigh Benard system has shown a marked reluctance to exhibit clear scaling in the energy or entropy spectrum. The recent numerical simulation of Pandey, Verma and Mishra has shown significantly better evidence of scaling in the infinite Prandtl number limit. This prompted us to look at this limit analytically. We find that the inevitable presence of sweeping helps give a very good understanding of the results of Pandey et. al. In the presence of rotation, the Rayleigh number dependence of the Nusselt number shows a strong increase in slope in recent experiments and simulations at finite Prandtl number. In the infinite Prandtl number case we find that this steepening does not occur for any rotation speed and our results satisfy the Doering-Constantin bound.