标题： 对对流的解析和数值线性分析的重新审视 显示英文标题

标题： Analytical and Numerical Linear Analyses of Convection Revisited

摘要： 我们对大于温度尺度高度的区域中的对流进行线性分析。 我们在这些分析中同时采用解析和数值方法。 在不考虑所有耗散的情况下，对流的典型时间尺度由温度尺度高度上的自由下落时间决定。 我们定量地展示了布西内斯克近似和温泽尔-克兰默-布里卢因（WKB）近似适用的条件。 我们重新评估了临界瑞利数，这是对流的一个关键指标，并表明WKB近似往往会低估临界瑞利数，尤其是在温度尺度高度与区域高度相当或更小时。 我们清楚地解释了为什么热传导和粘度都需要来稳定负熵梯度介质。 显示英文摘要

摘要： We conduct linear analyses of convection in domains larger than the temperature scale height. We employ both analytical and numerical methods in these analyses. In the case excluding all dissipation, the typical time scale of convection is determined by the free fall time over the temperature scale height. We quantitatively show the condition for the Boussinesq and Wentzel-Kramers-Brillouin (WKB) approximations to be applicable. We provide a reassessment of the critical Rayleigh number, a key indicator of convection, and show that WKB approximation tends to underestimate the critical Rayleigh number, particularly when the temperature scale height is comparable to or smaller than the domain height. We show clear explanation why both thermal conduction and viscosity are required for stabilizing negative entropy gradient medium.