Rigorous bounds on heat transport in rapidly-rotating Rayleigh Benard convection
Two approaches to rigorously estimating the heat transport in rapidly-rotating Rayleigh Benard convection are presented. The first uses the 'background method' of Constantin & Doering, and the second is a novel direct analysis of a class of exact solutions of the governing fluid equations. Both analyses are performed in the context of the asymptotically-reduced system of Julien, Knobloch, and Werne. The background method is used to prove an upper bound guaranteeing that the Nusselt number is bounded by a constant times the cube of the reduced Rayleigh number. The exact solutions, on the other hand, are shown to have Nusselt number scaling as a constant times reduced Rayleigh number to the 1.5 (modulo sub-algebraic factors).