Abstract We investigate the onset of average convection and its nonlinear regimes in a single-component fluid layer overlying a fluid-saturated porous layer. A heated from below cavity with a superposed fluid and a porous medium undergoes high-frequency and small-amplitude vertical vibrations in the gravitational field. Porosity of the medium decreases linearly with depth at a positive porosity gradient. Thermal vibrational convection equations are obtained by the averaging method and solved numerically. The shooting method, Galerkin method and finite-difference method are applied. It is shown that for small vibration accelerations, a convective flow is generated as short-wave rolls in the fluid layer overlying a porous medium. The heat flux undergoes abrupt changes as the supercriticality increases. It is due to the fluid flow penetrating into pores. A magnitude of the jump grows with the growth of vibration intensity. For sufficiently large vibration accelerations, the average convection is excited in the form of long-wave rolls that penetrate both layers. Here, the Nusselt number is 2–3 times higher than its value in the static gravity field.

中文翻译：

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垂直振动下叠加流体和多孔层中的非线性对流状态：正孔隙度梯度

摘要 我们研究了覆盖在流体饱和多孔层上的单组分流体层中平均对流的开始及其非线性机制。流体和多孔介质叠加的从下方加热的腔体在重力场中经历高频和小幅度的垂直振动。在正孔隙度梯度下，介质的孔隙度随深度线性下降。热振动对流方程通过平均法得到并数值求解。应用射击法、伽辽金法和有限差分法。结果表明，对于小的振动加速度，在覆盖多孔介质的流体层中会以短波滚动的形式产生对流。随着超临界度的增加，热通量发生急剧变化。这是由于流体流动渗透到孔隙中。跳跃的幅度随着振动强度的增加而增加。对于足够大的振动加速度，平均对流以穿透两层的长波卷的形式激发。此处，努塞尔数比其在静态重力场中的值高 2-3 倍。