Bounds on vertical heat transport for infinite-Prandtl-number Rayleigh-Benard convection

For the infinite-Prandtl-number limit of the Boussinesq equations, the enhancement of vertical heat transport in Rayleigh-Bernard convection, the Nusselt number Nu, is bounded above in terms of the Rayleigh number Ra according to Nu <= 0.644 x Ra-1/3 [log Ra](1/3) as Ra --> infinity. This result follows from the utilization of a novel logarithmic profile in the background method for producing bounds on bulk transport, together with new estimates for the bi-Laplacian in a weighted L-2 space. It is a quantitative improvement of the best currently available analytic result, and it comes within the logarithmic factor of the pure 1/3 scaling anticipated by both the classical marginally stable boundary layer argument and the most recent high-resolution numerical computations of the optimal bound on Nu using the background method.