Abstract

The onset of thermal convection in an anisotropic horizontal porous layer heated from below and rotating about vertical axis, under local thermal non-equilibrium hypothesis is studied. Linear and nonlinear stability analysis of the conduction solution is performed. Coincidence between the linear instability and the global nonlinear stability thresholds with respect to the L²—norm is proved.

Article Highlights

• A necessary and sufficient condition for the onset of convection in a rotating anisotropic porous layer has been obtained.

• It has been proved that convection can occur only through a steady motion. A detailed proof is reported thoroughly.

• Numerical analysis shows that permeability promotes convection, while thermal conductivities and rotation stabilize conduction.

中文翻译：

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使用 LTNE 旋转完全各向异性多孔介质的最佳稳定性阈值

摘要

在局部热非平衡假设下，研究了从下方加热并绕垂直轴旋转的各向异性水平多孔层中热对流的开始。执行传导解决方案的线性和非线性稳定性分析。证明了关于 L ^{2 -}范数的线性不稳定性和全局非线性稳定性阈值之间的一致性。

文章亮点

• 已经获得了旋转各向异性多孔层中开始对流的充分必要条件。

• 已经证明对流只能通过稳定的运动发生。详细的证明被彻底报告。

• 数值分析表明，渗透率促进对流，而热导率和旋转稳定传导。