Abstract The onset of thermal vibrational convection in a fluid layer overlaying a fluid-saturated porous layer is studied in zero gravity. A thermal gradient is imposed transverse to the layers. The two-layer system performs high-frequency small-amplitude oscillations perpendicular to the thermal gradient. We solve a linear stability problem with respect to the fluid quasi-equilibrium state. The basic closed-looped oscillatory flow with zero average velocity characterizes the quasi-equilibrium state. The average roll convection is generated if the Rayleigh number exceeds its threshold value. The bimodal marginal stability curves are revealed at different ratios of the fluid layer thickness to that of the porous layer. They are somewhat similar to the curves first obtained by Chen and Chen for the onset of thermal convection in a superposed fluid-porous layer in a gravity field. We find that short-wave convection replaces the long-wave one with an increase in the ratio of layer thicknesses. The transition is accompanied by a jump-wise increase in the wave number of the most dangerous convective rolls. However, the critical wave number of the vibrational convection rolls can change by several orders of magnitude in contrast to that of the gravitational convection rolls. So, one can have super short-wave convection in zero gravity. A value of the instability threshold varies non-monotonically. The convection onset delays rather weakly at small thickness ratios. On the contrary, sufficiently high thickness ratios make the convection onset speed up strongly.

中文翻译：

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失重条件下高频纵向振动叠加流体多孔层中热对流的开始

摘要 在零重力下研究了覆盖在流体饱和多孔层上的流体层中热振动对流的开始。横向于层施加热梯度。两层系统执行垂直于热梯度的高频小振幅振荡。我们解决了关于流体准平衡状态的线性稳定性问题。具有零平均速度的基本闭环振荡流表征准平衡状态。如果瑞利数超过其阈值，则会生成平均滚动对流。双峰边缘稳定性曲线在流体层厚度与多孔层厚度的不同比率下显示。它们有点类似于 Chen 和 Chen 首先获得的曲线，用于重力场中叠加的流体多孔层中的热对流开始。我们发现短波对流随着层厚比的增加取代了长波对流。这种转变伴随着最危险的对流滚动波数的跳跃式增加。然而，与重力对流辊的临界波数相比，振动对流辊的临界波数可以改变几个数量级。因此，人们可以在零重力下进行超短波对流。不稳定阈值的值非单调变化。在小厚度比下，对流开始延迟相当弱。相反，足够高的厚度比使对流开始加速强烈。