Bound on vertical heat transport at large Prandtl number

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• 作者：Xiaoming Wang
• 关键词：Rayleigh– ; Bé ; nard convection ; Boussinesq equations ; Prandtl number ; Rayleigh number ; Nusselt number
• 刊名：Physica D
• 出版年：2008
• 期刊代码：55_01672789
• 类别：ph
• 出版时间：15 May 2008
• 卷：237
• 期：6
• 页码：854-858
• 文件大小：278 K

摘要

We prove a new upper bound on the vertical heat transport in Rayleigh–Bénard convection of the form pan class="inlMMLBox">pan> under the assumption that the ratio of Prandtl number over Rayleigh number satisfies pan class="inlMMLBox">pan> where the non-dimensional constant c₀ depends on the aspect ratio of the domain only. This new rigorous bound agrees with the (optimal) pan class="inlMMLBox">pan> bound (modulo logarithmic correction) on vertical heat transport for the infinite Prandtl number model for convection due to Constantin and Doering [P. Constantin, C.R. Doering, Infinite Prandtl number convection, J. Stat. Phys. 94 (1) (1999) 159–172] and Doering, Otto and Reznikoff [C.R. Doering, F. Otto, M.G. Reznikoff, Bounds on vertical heat transport for infinite Prandtl number Rayleigh–Bénard convection, J. Fluid Mech. 560 (2006) 229–241]. It also improves a uniform (in Prandtl number) pan class="inlMMLBox">pan> bound for the Nusselt number [P. Constantin, C.R. Doering, Heat transfer in convective turbulence, Nonlinearity 9 (1996) 1049–1060] in the case of large Prandtl number.