  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.
