Absence of Evidence for the Ultimate Regime in Two-Dimensional Rayleigh-Bénard Convection
Absence of Evidence for the Ultimate Regime in Two-Dimensional Rayleigh-Bénard Convection
复制标题
缺乏二维瑞利-贝纳德对流终极状态的证据
DOI：
10.1103/physrevlett.123.259401
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发表时间：
2019
影响因子：
8.6
通讯作者：
Wettlaufer, J. S.
中科院分区：
文献类型：
--
作者：
Doering, C. R.;Toppaladoddi, S.;Wettlaufer, J. S.
Zhu等人[1]报告直接数值模拟的湍流热对流在二维平面无滑移等温壁和瑞利数（Ra）范围从10 8到10 14。对于努塞尔数（Nu），作者报告了10 13≤ Ra≤ 1014的四个数据点的Nu ≤ Ra 0.35的标度。他们还将Nu分解为来自空间域的“羽流喷射”（Nue）和“羽流影响”（Nui）区域的贡献，报告Nue = Ra 0。对于这四个数据点，将其解释为所谓的“终极”热对流制度的证据，其特征在于体积热传输缩放Nu Ra 1= 2模对数校正[2]。虽然关于边界层性质的假设[2]构成了这个系统的一个组成部分，但对流状态的基本特征是渐近的Nu-Ra关系[2-4]。Zhu等人[1]通过最后四个热通量数据[10 13≤ Ra≤ 10 14]绘制了一条任意线。当我们对这些数据进行客观最小二乘幂律拟合时，我们发现Nu= 0.035× Ra 0.332，其经验指数与1= 3（所谓的“经典”标度指数[5-7]）无法区分。此外，Ra= 10 8至10 13的数据通过前一拟合的外推得到了非常好的描述，Nu= 0.138× Ra 2= 7，107≤ Ra≤ 1010的高分辨率模拟[8]。事实上，这50年数据的幂律拟合产生标度指数0.289，与2= 7无法区分（小于1.2%）。将图1与参考文献1中的图1进行比较。[1]的文件。完整数据集与纯标度的明显偏差，加上Ra的有限范围（十年）和经典1= 3标度出现的数据集的小尺寸（只有四个点），排除了对渐近大Ra的明确外推。尽管如此，Zhu等人报告的2D热传输结果让人想起以前的3D模拟[9，10]和实验[11-13]，与从Nu Ra 2= 7到Nu Ra 1= 3的交叉一致，适用于2× 10 9和10 11之间的各种瑞利数。总之，虽然Zhu et al. [1]没有报告任何详细的统计分析，他们的数据，我们已经表明，
Zhu et al.[1] report direct numerical simulations of turbulent thermal convection in two dimensions with planar no-slip isothermal walls and Rayleigh numbers (Ra) ranging from 10 8 to 10 14. For the Nusselt number (Nu) the authors report a scaling of Nu∼ Ra 0.35 for the four data points with 10 13≤ Ra≤ 1014. They also decomposed Nu into contributions from “plume-ejecting”(Nue) and “plume-impacting”(Nui) regions of the spatial domain reporting Nue∼ Ra0. 38 for those four data points, interpreting this as evidence of a so-called “ultimate” regime of thermal convection characterized by bulk heat transport scaling Nu∼ Ra 1= 2 modulo logarithmic corrections [2]. Although hypotheses concerning the nature of boundary layers [2] constitute one ingredient of this system, the fundamental characterization of the state of convection is the asymptotic Nu-Ra relation [2–4]. Zhu et al.[1] drew an arbitrary line through the final four heat flux data [10 13≤ Ra≤ 1014]. When we perform an objective least-squares power law fit to these data we find Nu= 0.035× Ra 0.332 with an empirical exponent that is indistinguishable from 1= 3, the so-called “classical” scaling exponent [5–7].Moreover, the data from Ra= 10 8 to 10 13 are extremely well described by extrapolation of a previous fit, Nu= 0.138× Ra 2= 7, from high resolution simulations for 107≤ Ra≤ 1010 [8]. Indeed, the power law fit of those 5 decades of their data yields the scaling exponent 0.289, indistinguishable (less than 1.2%) from 2= 7. Compare Fig. 1 here to Fig. 1 of Ref.[1]. The clear deviation of the full dataset from pure scaling, combined with the limited range of Ra (one decade) and the small size of the dataset (just four points) over which the classical 1= 3 scaling appears, precludes definitive extrapolation to asymptotically large Ra. Nevertheless the 2D heat transport results reported by Zhu et al. are reminiscent of previous 3D simulations [9, 10] and experiments [11–13] consistent with crossovers from Nu∼ Ra 2= 7 to Nu∼ Ra 1= 3 for various Rayleigh numbers between 2× 10 9 and 10 11. In summary, while Zhu et al.[1] do not report any detailed statistical analysis of their data, we have shown