Our goal is to investigate fundamental properties of the system of internally cooled convection. The system consists of an upward thermal flux at the lower boundary, a mean temperature lapse-rate and a constant cooling term in the bulk with the bulk cooling in thermal equilibrium with the input heat flux. This simple model represents idealised dry convection in the atmospheric boundary layer, where the cooling mimics the radiative cooling to space notably through longwave radiation. We perform linear stability analysis of the model for different values of the mean stratification to derive the critical forcing above which the fluid is convectively unstable to small perturbations. The dynamic behavior of the fluid system is described and the scaling of various important measured quantities such as the total vertical convective heat flux and the upward mass flux is measured. We introduce a lapse-rate dependent dimensionless Rayleigh-number that determines the behavior of the system, finding that the convective heat-flux and mass-flux scale approximately as and respectively. The area-fraction of the domain that is occupied by upward and downward moving fluid and the skewness of the vertical velocity are studied to understand the asymmetry inherent in the system. We conclude with a short discussion on the relevance to atmospheric convection and the scope for further investigations of atmospheric convection using similar simplified approaches.

中文翻译：

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内部冷却对流的动力学和缩放

我们的目标是研究内部冷却对流系统的基本特性。该系统由下边界处的向上热通量、平均温度递减率和本体中的恒定冷却项组成，其中本体冷却与输入热通量处于热平衡。这个简单的模型代表了大气边界层中的理想化干对流，其中冷却模拟了空间辐射冷却，特别是通过长波辐射。我们对不同平均分层值的模型进行线性稳定性分析，以得出临界强迫，高于该临界强迫时，流体对小扰动对流不稳定。描述了流体系统的动态行为，并测量了各种重要测量量的缩放，例如总垂直对流热通量和向上质量通量。我们引入了一个与递减率相关的无量纲瑞利数来确定系统的行为，发现对流热通量和质量通量分别近似为 和 。研究向上和向下移动的流体所占据的域的面积分数和垂直速度的偏度，以了解系统固有的不对称性。最后，我们简短讨论了与大气对流的相关性以及使用类似简化方法进一步研究大气对流的范围。