Abstract A set of Direct Numerical Simulations in a heated square cavity invoking the Boussinesq approximation was carried out at Rayleigh numbers ranging between 10 8 and 10 11 and Prandtl number of 0.71. The three dimensional configurations studied represent an infinitely deep cavity, thus corresponding to a statistically two-dimensional flow with an imposed temperature varying linearly on the horizontal walls. In such configuration, the Rayleigh number, and therefore turbulence intensity, is the highest ever reached. The database presented herein includes first and second order statistical moments as well as full Reynolds stresses, turbulent heat fluxes and temperature variance budgets. The latter are extremely rare for buoyancy driven flow configurations and are therefore believed to be valuable to the turbulence modelling community. The analysis of the data collected thus focuses on aspects of relevance to the Reynolds averaged modelling of such flows. The effect of increasing the Rayleigh number on the flow statistics, Nusselt number predictions and thermal stratification is investigated. The most important aspect influencing the behaviour of the budgets was found to be the displacement of the position of the maximum of temperature variance towards the inner zone of the boundary layer. Such difference in behaviour between the thermal and velocity boundary layers introduces regions of negative production in the budgets that tend to increase with the Rayleigh number. The production of turbulence by buoyancy is also found to be of the same order of magnitude as other budget terms at all Rayleigh numbers.

中文翻译：

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瑞利数高达 1011 的充气差热方腔的直接数值模拟

摘要 在10 8 和10 11 之间的瑞利数和0.71 的普朗特数下，在加热方腔中进行了一组调用Boussinesq 近似的直接数值模拟。所研究的三维结构代表了一个无限深的空腔，因此对应于具有在水平壁上线性变化的外加温度的统计二维流动。在这种配置中，瑞利数以及湍流强度是有史以来最高的。此处提供的数据库包括一阶和二阶统计矩以及完整的雷诺应力、湍流热通量和温度变化预算。后者对于浮力驱动的流动配置极为罕见，因此被认为对湍流建模社区很有价值。因此，对收集到的数据的分析侧重于与此类流动的雷诺平均建模相关的方面。研究了增加瑞利数对流动统计、努塞尔数预测和热分层的影响。发现影响预算行为的最重要方面是温度变化最大值的位置向边界层内部区域的位移。热边界层和速度边界层之间的这种行为差异在预算中引入了负产生区域，这些区域往往随着瑞利数而增加。还发现浮力产生的湍流与所有瑞利数的其他预算项具有相同的数量级。