In this article, we study the stability and transition of couple stress fluid saturated porous media, heated from below and cooled from above by employing a thermal non-equilibrium model. Careful analysis shows that the thermal non-equilibrium model has a global attractor, and the global attractor only consists of the basic solution if the Rayleigh number is equal or below a threshold. In generic case where the transitioning eigenvalue has multiplicity one, we show that the transition involved is of continuous type, and the basic solution will be bifurcated to two stable convection solutions which attract globally. If the leading eigenvalue multiplicity is two, the transition is also continuous and a global attractor homeomorphic to the unit circle bifurcates. The attractor then contains four steady-state convection solutions, two of which are stable while the other two are unstable. Further numerical works give more details in the transition process including the bifurcated roll structure.

在本文中，我们采用热非平衡模型研究了从下方加热和从上方冷却的耦合应力流体饱和多孔介质的稳定性和转变。仔细分析表明，热非平衡模型具有全局吸引子，并且全局吸引子仅包含瑞利数等于或低于阈值的基本解。在过渡特征值具有多重性的一般情况下，我们表明所涉及的过渡是连续类型的，基本解将分为两个全局吸引的稳定对流解。如果前导特征值重数为 2，则过渡也是连续的，并且同胚于单位圆的全局吸引子分叉。吸引子包含四个稳态对流解，其中两个是稳定的，而另外两个是不稳定的。进一步的数值工作给出了过渡过程的更多细节，包括分叉辊结构。