We study the flow and thermal stratification of a closed domain subjected to different combinations of line and distributed surface heating and cooling. Our observations are drawn from a set of direct numerical simulations in which the ratio of the strength of the distributed sources to the localized sources $\mathrm{\Gamma }$ is varied and shown to play a decisive role in determining the system's statistically steady state. Domains of sufficient horizontal extent that are heated from below and cooled from above in equal amounts by two line sources ($\mathrm{\Gamma }=0$) produce a stable two-layer stratification. The planar plumes generated by each line source are connected by a large-scale circulation over the full depth of the domain and induce secondary circulations within each layer. As the distributed component of the heating, and therefore $\mathrm{\Gamma }$, increases, the buoyancy difference between the layers decreases, before being destroyed when $\mathrm{\Gamma }>1$. For increasing $\mathrm{\Gamma }\in [0,1]$, we observe an increasing tilt of the interface between the layers and the eventual disappearance of the secondary circulation cells. The mean buoyancy transport between the two layers of the stable stratification is dominated by the plumes for all $\mathrm{\Gamma }<1$ because the buoyancy flux associated with interfacial mixing is negligible. Building on existing approaches that typically assume uniform buoyancy within each layer, we develop a model that admits a lateral buoyancy gradient. The model predictions of the buoyancy difference between the layers, the tilt of the interface, and the large-scale circulation strength exhibit a reasonably good agreement with the direct numerical simulation data.

中文翻译：

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由线型和分布式浮力源组合驱动的受限湍流对流

我们研究了封闭区域的流动和热分层，该区域受线和分布表面加热和冷却的不同组合的影响。我们的观察结果来自一组直接数值模拟，其中分布式源与本地源的强度之比$\mathrm{\Gamma }$变化很大，并显示出在确定系统的统计稳定状态中起决定性作用。由两个线源从下方加热并从上方冷却的具有足够水平范围的区域（$\mathrm{\Gamma }=0$）产生稳定的两层分层。由每个线源产生的平面羽状流在区域的整个深度上通过大规模环流连接，并在每一层内引起次级环流。作为加热的分布式组件，因此$\mathrm{\Gamma }$增大时，各层之间的浮力差减小，然后在破坏时 $\mathrm{\Gamma }>\mathrm{1个}$。为了增加$\mathrm{\Gamma }\in [0，\mathrm{1个}]$，我们观察到各层之间的界面倾斜增加，并最终导致次级循环细胞消失。稳定分层的两层之间的平均浮力传输主要由所有羽状流形成。$\mathrm{\Gamma }<\mathrm{1个}$因为与界面混合相关的浮力通量可以忽略不计。在通常假定每一层内都具有均匀浮力的现有方法的基础上，我们开发了一个允许横向浮力梯度的模型。层之间的浮力差，界面的倾斜度和大尺度环流强度的模型预测与直接数值模拟数据具有相当好的一致性。