Abstract
For the infinite-Prandtl-number limit of the Boussinesq equations, the enhancement of vertical heat transport in Rayleigh-Benard convection, the Nusselt number Nu, is bounded above in terms of the Rayleigh number Ra according to Nu≤0.644× Ra 1/3 [log R a ] 1/3 as R a → ∞. 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.
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