Abstract We consider the case of a tall differentially heated cavity (containing air) for which the buoyancy flow is in the so-called boundary-layer regime (displaying thin regions featured by strong temperature gradients adjacent to the vertical walls and thermally stratified fluid in the centre). By using a numerical method able to account for compressibility and variable viscosity effects, we investigate the response of such a system to the application of temperature differences in a range of characteristic numbers for which the resulting flow is expected to be time-periodic or highly time-dependent. More precisely, the problem is examined by allowing both the Rayleigh number and the inclination (θ) of this configuration with respect to the vertical direction to span relatively wide intervals (1.8 × 105 ≤ Ra ≤ 3 × 106, −90° ≤ θ ≤ 90°). Insights into the influence of variable thermodynamic properties are obtained by comparing such numerical results with equivalent simulations based on the classical Boussinesq approximation. The evolution of the considered system towards a fully turbulent state is also discussed to a certain extent.

中文翻译：

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关于倾斜差热腔内可压缩热对流的振荡模式

摘要 我们考虑了一个高差热腔（包含空气）的情况，其中浮力流处于所谓的边界层状态（显示以与垂直壁相邻的强温度梯度和热分层流体为特征的薄区域）。中心）。通过使用能够解释可压缩性和可变粘度效应的数值方法，我们研究了这种系统对应用一系列特征数中的温差的响应，对于这些特征数，预期产生的流动是时间周期的或高度时间的-依赖。更准确地说，通过允许此配置相对于垂直方向的瑞利数和倾角 (θ) 跨越相对较宽的区间 (1.8 × 105 ≤ Ra ≤ 3 × 106，-90° ≤ θ ≤ 90°）。通过将此类数值结果与基于经典 Boussinesq 近似的等效模拟进行比较，可以深入了解可变热力学性质的影响。在一定程度上还讨论了所考虑的系统向完全湍流状态的演变。