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Convective turbulence in a Rayleigh Benard system has shown a markedreluctance to exhibit clear scaling in the energy or entropy spectrum. Therecent numerical simulation of Pandey, Verma and Mishra has shown significantlybetter evidence of scaling in the infinite Prandtl number limit. This promptedus to look at this limit analytically. We find that the inevitable presence ofsweeping helps give a very good understanding of the results of Pandey et. al.In the presence of rotation, the Rayleigh number dependence of the Nusseltnumber shows a strong increase in slope in recent experiments and simulationsat finite Prandtl number. In the infinite Prandtl number case we find that thissteepening does not occur for any rotation speed and our results satisfy theDoering-Constantin bound.

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