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- W2007483713 abstract "For the infinite-Prandtl-number limit of the Boussinesq equations, the enhancement of vertical heat transport in Rayleigh–Bénard convection, the Nusselt number $hbox{it Nu}$, is bounded above in terms of the Rayleigh number $hbox{it Ra}$ according to $hbox{it Nu},{le},0.644 ,{times}hbox{it Ra}^{{1}/{3}} [log{hbox{it Ra}}]^{{1}/{3}}$ as $hbox{it Ra},{rightarrow},infty$. 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 $hbox{it Nu}$ using the background method." @default.
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- W2007483713 date "2006-07-20" @default.
- W2007483713 modified "2023-10-14" @default.
- W2007483713 title "Bounds on vertical heat transport for infinite-Prandtl-number Rayleigh–Bénard convection" @default.
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- W2007483713 doi "https://doi.org/10.1017/s0022112006000097" @default.
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