标题： 突然冷却的流体层中非渗透对流的开始 显示英文标题

标题： The onset of nonpenetrative convection in a suddenly cooled layer of fluid

摘要： 在水平Boussinesq流体层受到温度阶跃变化的情况下，使用传播理论研究了非穿透对流的起始条件。考虑了广泛的普朗特数和两种不同的运动学边界条件。结果表明，对于高瑞利数，对流运动起始的临界条件正好再现了非定常雷诺-贝纳德不稳定的临界条件。目前的结果扩展了以前的研究，并显示在低普朗特数下，刚性-刚性和自由-刚性临界曲线有趋同的趋势。使用不同方法对不稳定起始条件和起始时间的当前结果与之前报告的结果进行比较，在中等至高普朗特数范围内取得了良好的一致性。建议在无应力边界系统中，实验测得的和理论预测的起始时间的比值为10。 显示英文摘要

摘要： Conditions for the onset of nonpenetrative convection in a horizontal Boussinesq fluid layer subject to a step change in temperature are studied using propagation theory. A wide range of Prandtl numbers and two different kinematic boundary conditions are considered. It is shown that for high Rayleigh numbers, critical conditions for the onset of convective motion reproduce exactly those for the unsteady Rayleigh-B\'enard instability. Present results extend those of previous research and show a tendency of the rigid-rigid and free-rigid critical curves to converge for low Prandtl numbers. Comparison between present and previously reported results on critical conditions for the onset of instabilities and onset time using different methods yields good agreement on a middle to high Prandtl number range. A ratio of 10 between experimentally measured and theoretically predicted onset times is suggested for stress-free bounded systems.