Bounds on vertical heat transport for infinite-Prandtl-number Rayleigh–Bénard convection
Bounds on vertical heat transport for infinite-Prandtl-number Rayleigh–Bénard convection
复制标题
DOI：
10.1017/s0022112006000097
复制
发表时间：
2005-11
影响因子：
3.7
通讯作者：
C. Doering;F. Otto;Maria G. Reznikoff
中科院分区：
文献类型：
--
作者：
C. Doering;F. Otto;Maria G. Reznikoff
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.
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.