Rayleigh–Bénard convection: Improved bounds on the Nusselt number
Rayleigh–Bénard convection: Improved bounds on the Nusselt number
复制标题
瑞利-贝纳德对流：改进努塞尔数的界限
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Christian Seis
中科院分区：
文献类型：
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作者：
Felix Otto;Christian Seis
我们认为Rayleigh-Benard对流是由无限普朗特数极限下的Boussinesq方程模拟的。我们感兴趣的是平均向上热量输送Nu和无量纲化温度强迫Rayleigh数Ra之间的比例关系。实验、渐近性和启发式表明，Nu∼Ra1/3。这项工作主要是受到早期关于Nu关于Ra的上界的两个严格工作的启发。(1)Constantin和Doering在Stokes方程水平上利用L≲的最大正则性估计(对数失效)建立了Nu Ra1/3LN∞2/3ra的工作。(2)Doering、Reznikoff和第一作者利用背景场方法建立了Nu≲Ra1/3LN 1/3ra。本文包含两个结果。(1)背景场方法可稍作修改，得到Nu≲Ra1/3LN 1/15Ra。(2)背景场方法后的估计可与L∞的最大正则性相结合，得到Nu≲Ra1/3LN 1/3LN Ra.
We consider Rayleigh–Benard convection as modelled by the Boussinesq equations in the infinite-Prandtl-number limit. We are interested in the scaling of the average upward heat transport, the Nusselt number Nu, in terms of the non-dimensionalized temperature forcing, the Rayleigh number Ra. Experiments, asymptotics and heuristics suggest that Nu ∼ Ra1/3. This work is mostly inspired by two earlier rigorous work on upper bounds of Nu in terms of Ra. (1) The work of Constantin and Doering establishing Nu ≲ Ra1/3ln 2/3Ra with help of a (logarithmically failing) maximal regularity estimate in L∞ on the level of the Stokes equation. (2) The work of Doering, Reznikoff and the first author establishing Nu ≲ Ra1/3ln 1/3Ra with help of the background field method. The paper contains two results. (1) The background field method can be slightly modified to yield Nu ≲ Ra1/3ln 1/15Ra. (2) The estimates behind the background field method can be combined with the maximal regularity in L∞ to yield Nu ≲ Ra1/3ln 1/3ln Ra —...