A simple system for moist convection: the Rainy–Bénard model
A simple system for moist convection: the Rainy–Bénard model
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湿对流的简单系统：Rainy-Bénard 模型
DOI：
10.1017/jfm.2018.954
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发表时间：
2018
影响因子：
3.7
通讯作者：
S. Tobias
中科院分区：
文献类型：
--
作者：
G. Vallis;D. Parker;S. Tobias
瑞利-巴萨姆德对流是流体力学中研究得最多的模型之一。大气对流是气候系统中最重要的组成部分之一，相比之下，它是复杂的，而且人们对它知之甚少。大气对流的一个关键属性是水蒸气凝结提供的浮力源，但辐射、可压缩性、液态水和冰的存在使系统和我们对它的理解进一步复杂化。本文采用理想气体方程的Boussinesq极限，加入符合简化克劳修斯-克拉珀龙关系的凝结物，给出了一种理想的湿对流模型。该系统允许在基本水平上探索湿对流，如果冷凝潜热为零，则可简化为经典的瑞利-巴姆纳德模型。该模型有一个精确的、瑞利数无关的“毛毛雨”解决方案，其中水蒸气从饱和的低表面扩散通过冷凝来平衡，温度场（以及水分的饱和值）由冷凝中释放的热量自一致地决定。这种状态是经典问题中导电溶液的湿润模拟。我们用数值方法确定了该解作为瑞利数和无因次潜热参数的函数的线性稳定性。在瑞利数和非量纲凝聚参数的不同值下，我们还给出了一些二维、时变的非线性解。当瑞利数足够低时，系统收敛于细雨解，我们没有发现在该解稳定时二维自持续对流可以发生的证据。随着瑞利数或凝结效应的增加，流从稳定过渡到湍流，由其他羽流发出的重力波触发羽流。随着湍流水平的增加，内部变得干燥，因为羽流夹带了更多的干燥空气，而且由于顶部饱和的边界层变得更薄。气流在区域内部形成广泛的相对湿度最小值，当瑞利数较高时，相对湿度最小值与瑞利数的关系较弱。
Rayleigh–Bénard convection is one of the most well-studied models in fluid mechanics. Atmospheric convection, one of the most important components of the climate system, is by comparison complicated and poorly understood. A key attribute of atmospheric convection is the buoyancy source provided by the condensation of water vapour, but the presence of radiation, compressibility, liquid water and ice further complicate the system and our understanding of it. In this paper we present an idealized model of moist convection by taking the Boussinesq limit of the ideal-gas equations and adding a condensate that obeys a simplified Clausius–Clapeyron relation. The system allows moist convection to be explored at a fundamental level and reduces to the classical Rayleigh–Bénard model if the latent heat of condensation is taken to be zero. The model has an exact, Rayleigh-number-independent ‘drizzle’ solution in which the diffusion of water vapour from a saturated lower surface is balanced by condensation, with the temperature field (and so the saturation value of the moisture) determined self-consistently by the heat released in the condensation. This state is the moist analogue of the conductive solution in the classical problem. We numerically determine the linear stability properties of this solution as a function of Rayleigh number and a non-dimensional latent-heat parameter. We also present some two-dimensional, time-dependent, nonlinear solutions at various values of Rayleigh number and the non-dimensional condensational parameters. At sufficiently low Rayleigh number the system converges to the drizzle solution, and we find no evidence that two-dimensional self-sustained convection can occur when that solution is stable. The flow transitions from steady to turbulent as the Rayleigh number or the effects of condensation are increased, with plumes triggered by gravity waves emanating from other plumes. The interior dries as the level of turbulence increases, because the plumes entrain more dry air and because the saturated boundary layer at the top becomes thinner. The flow develops a broad relative humidity minimum in the domain interior, only weakly dependent on Rayleigh number when that is high.